Koepka carded a closing 67 to finish 16 under par, matching the tournament scoring record set by Rory McIlroy at Congressional in 2011.
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 majors, 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.”