One of the most successful drivers of the current era, Power added the glaring omission to his resume by leading home pole-sitter Ed Carpenter and Dixon.
The Kiwi struggled for outright pace and opted to pit early on lap 161 taking a punt on another caution falling in the final 100 miles of the race and making full use of his renowned ability to save fuel.
The strategy worked as he started the final dash to the chequered flag in contention but didn't have enough to match Power.
"Man I just can't believe it," the 37-year-old Power said. "I can't thank Roger Penske, Verizon and my parents enough for allowing me to get to this point.
"I couldn't stop screaming on the radio.
"I was screaming with one to go that I had this.
"I was wondering if I would ever win this. I have had so many wins and so many poles but everyone talks about the 500 and I wanted it. I just couldn't imagine winning a race in front of this many people.
"It is just amazing."
As was the case for the past two years the race stayed green beyond the first quarter. The first caution came when defending champion Takuma Sato collided with a very slow James Davison.
Former NASCAR star Danica Patrick crashed out of the race on lap 68 bringing an end to her competitive career. She returned to this year's Indianapolis 500 for a cameo appearance seven years after leaving the sport to move to NASCAR.
Three-time winner Helio Castroneves was another to feel the bite of the Brickyard, crashing with a quarter of the race remaining.
Another former winner Tony Kanaan led a number of laps in the first half of the race but a puncture saw him lose a lap and fall out of contention before a late crash ended his race early.
