The big-hitting 27-year-old fired six birdies and a solitary bogey to finish four shots ahead of overnight leader Brian Harman and Japan's Hideki Matsuyama, whose closing 66 will take him to a career-high second in the world rankings.
Only McIlroy and Tiger Woods had previously finished double digits under par in the game's toughest test, while no runner-up had ever managed such a total.
Fleetwood, who had made the cut in just one of his previous seven major appearances, finished alone in fourth on 11 under following a final round of 72 with Rickie Fowler, Bill Haas and Xander Schauffele a shot further back in fifth.
"I've never contended for a major before, so when you get to Saturday and Sunday you've got to see how you react and how you feel," said Fleetwood, who bounced back from three bogeys in six holes on the front nine to birdie the ninth and 14th.
"I felt on Saturday I played great. Today my game wasn't quite there, but still got it round in level par. I scrapped a little bit for it, but I felt fine. I felt comfortable.
"I enjoyed playing late on Saturday and Sunday and then next time, whenever that comes, I know that inside myself I feel fine and I can contend for the victory."
Fleetwood was world No. 188 last September, but has reaped the rewards of returning to his former coach Alan Thompson and employing his friend Ian Finnis -- the husband of former England women's goalkeeper Rachel Brown-Finnis -- as his caddie.
And the 26-year-old from Southport, who finished a shot ahead of world No. 1 Dustin Johnson to claim his second European Tour title in Abu Dhabi in January, paid tribute to Finnis.
"He actually started caddying for me a year ago next week, so this was our anniversary I feel," Fleetwood added.
"When he started I couldn't hit it and I was missing cuts for fun. A year on we were playing late on a Sunday in a major, so that's a nice way to cap it off.
"He's brilliant. He'd never really done that before when he started coming on my bag. But I think what was underestimated was how well he knew me, how well he knew my game.
"He loves golf himself. He's a good golfer himself. And all of those things put together makes him a great caddie for me. I can't fault his work ethic, which is a massive part of it for me."