The 62nd 500 Mile International Sweepstakes was held at the Indianapolis Motor Speedway in Speedway, Indiana on Sunday, May 28, 1978. Danny Ongais dominated the early stages of the race but eventually dropped out with a blown engine. Al Unser Sr. dominated the second half, and held a large lead late in the race. However, Unser bent the front wing of his Lola during a pit stop on lap 180, causing his handling to go away over the final twenty laps. Second place Tom Sneva charged to catch Unser's crippled Lola but came up 8 seconds short at the finish line – the second-closest finish in Indy history to that point. Unser held off the challenge, and became a three-time winner of the 500. It was Al Unser's third Indy victory in the decade of the 1970s, and the fifth of nine overall victories by the Unser family.

Al Unser Sr. entered the month having won the 1977 California 500 at Ontario the previous September. Later in the 1978 season, Unser would go on to win the Pocono 500 and the California 500 again, sweeping the "triple crown" of Indy car racing for 1978. As of 2015 (the last year there was a "Triple Crown") Unser is the only driver in history to win all three 500-mile "triple crown" races in the same season, and coupled with the win at Ontario in 1977, set a record by winning four straight 500-mile Indy car races.

Second year driver Janet Guthrie finished ninth, and it was later revealed she drove with a fractured wrist. It was the highest finish for a female driver in Indy history until Danica Patrick finished in fourth place in 2005. During time trials, Tom Sneva, who had broken the barrier a year earlier, bettered his own record. This time he managed to complete all four qualifying laps over , setting once again new one-lap and four-lap track records.

Tony Hulman, the popular owner and president of the track since 1945, died the previous October. His widow Mary F. Hulman was named the chairperson of the board of the Speedway, and for the first time she delivered the famous starting command. Along with the death of Tony Hulman, the race was held just five weeks after eight USAC officials were killed in a plane crash. With dissent increasing among the participants about organizational issues and poor revenue, the 1978 race would be the final Indy 500 contested prior to the formation of CART and prior to the first open wheel "split."

Al Unser's victory was the first Indy triumph for the Cosworth DFX V8 engine. The British-based engine building company would go on to win the Indianapolis 500 for ten consecutive years.

Race schedule Race schedule – May, 1978SunMonTueWedThuFriSat  1  2  3  4  5  6Practice 7Practice 8Practice 9Practice10Practice11Practice12Practice13Time Trials14Time Trials15Practice16Practice17Practice18Practice19Practice20Time Trials21Time Trials22 23 24 25Carb Day26Mini-Marathon27Parade28Indy 50029Memorial Day30 31     Color Notes Green Practice Dark Blue Time trials Silver Race day Red Rained out* Blank No track activity * Includes days where trackactivity was significantlylimited due to rain

Practice and time trials For 1978, the turbocharger "boost" settings were set at 80 inHg, the same regulations used in 1974–1975 and 1977. The first weekend of time trials was scheduled for May 13–14. Rain, however, washed out the entire first weekend. Pole qualifying was moved to Saturday May 20.

Practice On Wednesday May 10, Mario Andretti turned a practice lap of , faster than the track record. Minutes later, Danny Ongais upped the best speed to . On Thursday May 11, rookie Rick Mears also joined the coveted "200 mph club" in practice. Johnny Rutherford () and A. J. Foyt () were also within striking distance.

On Friday May 12, the final day of practice before pole qualifying was scheduled to be held, Mario Andretti shattered the unofficial track record, turning a lap of . Also over were Mears, Rutherford, and Foyt. Tom Sneva, the driver who broke the 200 mph barrier a year earlier, was the slowest of the three Penske cars, managing only a lap during practice.

The rainout of time trials complicated the schedule for Mario Andretti. He was forced to leave the track and fly to Zolder for the Belgian Grand Prix which he won driving the Lotus 79 for the first time. Arrangements were being made for another driver to qualify the car for him, and he would return to the cockpit for race day. With no track activity possible at Indy for Sunday, A. J. Foyt flew to Talladega and finished third in the NASCAR Winston 500.

During the second week of practice, Pancho Carter and Tom Sneva joined the "200 mph club." Sneva had a hand-timed lap of about , inching closer to Andretti's mark from the previous week. Danny Ongais destroyed his primary car in a crash in turn four on Tuesday May 16. He was not seriously injured, but would have to qualify with his back-up car.

Pole Day – Saturday May 20

Since the first two days of time trials were rained out, pole qualifying was moved to the third day (May 20). The field was allowed one trip through the original qualifying draw order. Each car would be guaranteed an opportunity for one attempt during pole round. As soon as they reached the end of the qualifying draw, the pole position round would be concluded, and the "Third Day" of qualifying would commence.

Pole day dawned with temperatures in the high 70s and low 80s. Qualifying started promptly at 11:00 a.m., with Johnny Rutherford first out on the track. He fell short of the 200 mph barrier on all four laps, and settled for an average of .

At 12:03 p.m., Tom Sneva took to the track. Following in his own footsteps from the previous year, he set new all-time one-lap and four-lap track records, becoming the first driver in Indy history to complete all four qualifying laps over 200 mph. Lap 1 – 44.20 seconds, (new 1-lap track record) Lap 2 – 44.43 seconds, Lap 3 – 44.60 seconds, Lap 4 – 44.85 seconds, Total – 2:58.08, (new 4-lap track record) Due to changes in the rules in subsequent years, Sneva's one-lap and four-lap track records would stand until 1982. Sneva's four-lap average secured the pole position, his second pole in a row.

Sneva's Penske teammate, rookie Rick Mears, was the next car out. Mears completed three laps over 200 mph, and his four-lap average of was a rookie speed record, and would be good enough for the front row.

Janet Guthrie returned for her second start, and qualified strongly at . At 12:39 p.m., Danny Ongais made it an "all 200 mph" front row, securing second starting position at .

After practicing over 200 mph, A. J. Foyt was forced to wave off his run, and missed his chance at qualifying during the pole round. Mike Hiss was hired by Penske to drive substitute for Mario Andretti during time trials. Hiss qualified the car with a respectable speed of to rank 8th. However, on race day, Andretti would get back in the car, and he would be forced to line up in the 33rd starting position due to the driver switch.

Rain late in the day hampered the qualifying attempts. The trip through the original qualifying line exhausted at 5 p.m., and Tom Sneva officially secured the pole position. Several drivers including Bobby Unser, A. J. Foyt, and Pancho Carter, were unable to qualify during the pole round. At 5 p.m., the "third day" of time trials officially commenced, and those drivers would line up behind the cars from the pole round.

The day ended with the field filled to twenty cars. Bobby Unser finished his run in the rain as the lone "third day" qualifier. The track was closed for the day as soon as Unser returned to the pits at 5:11 p.m.

Bump Day – Sunday May 21 The final day of time trials opened with 13 spots unfilled. A. J. Foyt at was the fastest driver of the day. His speed was tied for second-fastest, but as a final day qualifier, he would line up 20th.

Roger Rager was the only major on-track incident of the day. At 3:53 p.m., on his second warm-up lap, he hit the outside wall in turn four, suffering an injured hand. Rager would miss the race. After a wave off on Saturday, Larry "Boom Boom" Cannon went out for his second attempt. He spun and brushed the wall on his second qualifying lap, and had to abort the run. Later on his third and final attempt, he was too slow to bump his way into the field. Dick Simon brushed the wall on the main stretch shaking down a car for Bill Puterbaugh. The car lost two wheels and it was too late in the day for the car to be repaired.

In the final hour, there was one spot left in the field when Bob Harkey was preparing to make his attempt. Jim Hurtubise, who had once again entered his now-infamous Mallard/Offy front-engined car, had been denied the permission to qualify, due to lack of speed. USAC had decided to set a minimum speed in order to pass "final" inspection, receive the appropriate sticker, and be allowed to make a qualifying attempt. They deemed Hurtubise ineligible, claiming he had not broken , despite some claiming he had lapped over . Hurtubise considered the ruling a personal harassment, lies, and an effort by USAC, Goodyear, and the Speedway to single him out and keep him from qualifying. After being a popular fixture amongst the fans for many years, several episodes of antics had caused some to begin to view Hurtubise unfavorably. Hurtubise got into a heated exchange with chief steward Tom Binford, then proceeded to climb into Harkey's car, shouting "If I can't qualify, no one can!" After a few minutes, Hurtubise was coaxed out of the car, and Harkey climbed in to crank it up. With some encouragement from the crowd, Hurtubise then jumped in front of Harkey, preventing him from pulling out of the pits. He had to be restrained by safety patrol members, and Harkey managed to pull away. While Harkey was on the backstretch of his warm-up lap, Hurtubise jumped over the pit wall and ran out on the race track in order to disrupt and halt the qualifying attempt. Running down the main stretch, several guards chased after him. Hurtubise was tackled by John Martin and was then detained by police. By this time, the crowd's opinion had changed, and they began booing and jeering Hurtubise for going too far by disrupting qualifying. Hurtubise was banned from the track for the remainder of the month.

Harkey managed to finish his qualifying attempt without incident, but his speed was not fast enough to stand. Within twenty minutes, Harkey was bumped by Joe Saldana. The day closed with Cliff Hucul bumping Graham McRae with two minutes left in the day.

After missing time trials, Mario Andretti won the Grand Prix of Belgium. He traveled back to Indianapolis during the week, and would be back in time for Carburetion Day "tests."

Carburetion Day The final practice was held on Thursday May 25. A. J. Foyt turned a fast lap of 199.468 mph, but then shut the engine off due to an oil line problem. He coasted to stop and required a tow-in. Gary Bettenhausen skipped the session as the crew was installing a new engine. Joe Saldana also failed to turn any laps as his crew was putting the finishing touches on a new engine install. Mario Andretti returned from Belgium and turned a lap of 192.719 mph, the third-fastest of the day. No incidents were reported.

Pit Stop Contest The elimination rounds for the 2nd annual Miller Pit Stop Contest were held Thursday May 25. Eight teams qualified for the contest during preliminary trials on May 17–18. Johnny Rutherford (12.89 seconds) was the fastest qualifier, with Wally Dallenbach (19.86 seconds) ranking second, and Al Loquasto (20.53 second) third. The other qualifiers included Larry Dickson (20.85 seconds), Johnny Parsons (20.89), Roger McCluskey, Pancho Carter, and Bobby Olivero. However, Olivero was later replaced by Mike Mosley. Loquasto was bumped from the race starting lineup, but stayed to compete in the pit stop contest.