Contenders Tom Sneva and Mario Andretti dropped out of the race in the second half, leaving Mears alone two laps ahead of the field, and he cruised to the victory.
Three months after the race, however, Mears would suffer severe leg injuries in a practice crash at Sanair.
The race is well-remembered for the terrible crash of sportswriter-turned-racer, Pat Bedard, who tumbled through the infield in turn 4 on lap 58.
The race was sanctioned by USAC, and was included as part of the 1984 CART PPG Indy Car World Series.
Defending race winner Tom Sneva, who broke the 200 mph barrier during time trials in 1977, headlined qualifying on pole day.
Sneva made history once again, as he became the first driver to break the 210 mph barrier, en route to his third pole position.
This Indy 500 was the last for 33 years that an active Formula One driver, Teo Fabi, featured in the field, with double World Champion Fernando Alonso making his 500 debut in 2017.
He coasted across the finish line powerless to complete the run, but the average speed sank to 207.467 mph.
Johnny Rutherford went out for his second attempt in a Foyt entry, but never completed a lap due to mechanical problems.
With rain in the forecast for Sunday, several teams scrambled to get their cars prepared to qualify on this day.
At 5:50 p.m., with only ten minutes left before the 6 o'clock gun, Johnny Rutherford took to the track for one last attempt to qualify.
His speed dropped over the final three laps, but his four-lap average of 202.062 mph was fast enough to bump his way into the field.
Jacques Villeneuve, who suffered a crash during practice, withdrew from the starting field after being ruled medically unfit to drive.
The top four race qualifiers and their respective pit crews were automatically eligible: Tom Sneva, Howdy Holmes, Rick Mears, and Michael Andretti.
The preliminary pairings were as follows: Sneva vs. Gloy, Holmes vs. Fabi, Mears vs. Simon, and Andretti vs. Holbert.
Andretti and his KRACO Racing team won the finals, the first rookie driver to win the event.
Mary F. Hulman gave the command to start engines just before 11 a.m., and all cars pulled away for the pace laps.
Pole sitter Tom Sneva settled into second, and rookie Michael Andretti went from the inside of row 2 to take third.
After 37 laps, race rookie and future two-time winner Emerson Fittipaldi dropped out due to low oil pressure.
The two-time Formula One World Champion had a relatively quiet month of May, acclimating himself gradually to the Indy car circuit.
Under the caution, Danny Sullivan came up too fast and ran into the car of Roberto Guerrero, hopping up on two wheels, and damaging his right-front suspension.
After the lengthy caution for Bedard's crash, Tom Sneva came to the lead, and led at the halfway point.
With Rick Mears now leading, Mario Andretti started slipping in the standings due to a broken exhaust pipe.
After running in the top five most of the day, Al Unser Jr. dropped out on lap 131 with a broken water pump.
With several contenders dropping out in quick succession, the race came down to two drivers in the final 100 miles: Rick Mears and Tom Sneva.
The only battle remained for second place, between Roberto Guerrero and Al Unser Sr. A light drizzle started entering the area in the final 30 laps or so, threatening to end the race early.
[10] After an eventful day - nearly being caught up in the Bedard crash, being hit by Sullivan during the ensuring yellow flag, overshooting his pit stall during one of his stops, and spinning in turn two - Guerrero was surprised to find out he finished second, and was voted co-Rookie of the Year.
Luke Walton introduced the starting command during the pre-race ceremonies, but did not have on-air duties during the race itself.
Jackie Stewart served as the host position in "ABC Race Central" for the final time.
The race was televised in Brasil for the first time, as the debut of former Formula One champion Emerson Fittipaldi attracted national interest.