Montoya, who won his Indy 500 debut in 2000, survived an early collision that forced him into the pits and dropped him to 30th place before mounting a stirring charge and storming to a one-car length win
"When I came through the field, I knew I had a really great car. But it was hard," said Montoya. "Oh my God! That was awesome."
"This is what racing and IndyCar is all about. Awesome racing all the way down to the wire."
Returning to IndyCar last year after stints in NASCAR and Formula One, Montoya took the lead with four laps to go and fought off a challenge from Australian Will Power. American Charlie Kimball was third.
The IndyCar Series win was his fourth, two coming at the sprawling 2.5 mile speedway.
The victory was also 16th for team owner Roger Penske, giving him the rare Daytona 500-Indy 500 double.
After a crash filled buildup to the race, a mix of excitement and apprehension hung over the famed Brickyard as the 33-car field took the command to start their engines.
The trepidation proved well placed with cars driven by Sage Karam and Takuma Sato coming together in the first corner of the opening lap, bringing out the yellow flag.
Problems continued on the restart when Simon De Silvestro, one of two women in the field, ran into the back of Montoya sending both drivers into the pits for repairs.
After last year's race went 149 laps without a caution flag, the first 11 laps of the 99th edition were run under yellow before the field finally settled into a rhythm with Ganassi team mates pole sitter Scott Dixon and 2013 winner Tony Kanaan setting the pace.
With 100 miles to go, the race had boiled down to a battle between IndyCar's two powerhouse outfits with Penske and Ganassi cars occupying the top six places.
A spectacular crash involving Stefano Coletti, Jack Hawksworth and Sebastian Saavedra brought out the final yellow of the day. That set up a wild sprint for the checkered flag, Montoya blasting past Dixon and Power and staying in front the final four laps as the crowd of close to 250,000 stood and roared.
"I was trying to keep the lead because I knew, with the heat, the tires would degrade and eventually they wouldn't be able to go round," said Power, the reigning IndyCar series champion. "Montoya got that last run and maybe I was a bit nice to him into turn one and lifted.
"That was serious racing there, it was a lot of fun.
"Full credit to the team, finishing one-two. Congrats to Juan, he was very strong all day and had to come through the field."
