The double US Open champion and Scott were tied for the lead with four holes remaining, with Woods just one behind and two holes ahead, but Koepka then holed pivotal birdie putts on 15 and 16 and held on to claim his third win of the last seven majors by a two-shot margin.
Gallant charges from Open champion Francesco Molinari and Ryder Cup hopeful Thomas Pieters came up just short, while the likes of Justin Thomas and Rickie Fowler were unable to keep pace with the leaders down the stretch.
Koepka’s impressive composure under huge pressure enabled him to become only the fifth player in history after Woods, Jack Nicklaus, Ben Hogan and Gene Sarazen to win the US Open and the PGA Championship in the same year, and he is also just the fifth American to win at least three majors before the age of 29.
Armed with a two-shot lead overnight, Koepka made a confident start when he holed from eight feet for birdie at the first, but he opened the door for the chasing pack when errant drives at the fourth and fifth led to bogeys and trimmed his advantage to one.
But as the leaderboard became increasingly congested behind him, with 30 players within five shots of the lead midway through the round, Koepka proved his major quality as he bounced back with three consecutive birdies from the seventh which capped an outward 33.
However, after good par saves at 10 and 11, Koepka missed great birdie chances on the next two greens and suddenly found himself tied for the lead with a resurgent Scott, who holed from six feet at the 13th for his fifth birdie in seven holes around the turn.
Woods, meanwhile, kept himself in the hunt for a first major victory in over 10 years as he turned in 32 with four birdies and one bogey, and he pulled within one of Koepka with further gains at 12 and 13 to set the pulses racing among the vast galleries following the 42-year-old.
The 14-time major champion lipped out for par at 14 before clawing the shot back when he knocked a stunning second to within a foot of the hole at the 15th, but Woods’ chances effectively ended as he carved his drive into the hazard to the right of the long 17th.
Woods’ ball avoided the water and gave him the chance to gouge it back into the fairway but, needing a birdie to have any chance of catching Koepka, he tugged his third into a greenside bunker and eventually did well to save par from 10 feet.
He did raise the roof one more time when he drained a 20-foot putt for a closing birdie on 18 to card a 64 and finish on 14 under, but Woods’ lowest final round of his major career was not enough to deny the nerveless Koepka.
After atoning for his earlier misses with birdie putts from 10 feet and six feet on 15 and 16, Koepka offered a glimmer of hope to playing-partner Scott when he misread his putt for a four on the 17th, but the Australian could not take advantage as he lipped out from close range.
Scott, who had posted only one top-10 in his last 13 major starts, then pulled his drive way left at the last and could not salvage a par to ensure that Woods finished alone in second place, with Scott’s 67 leaving him three adrift of the champion.
His final-hole struggles eased the pressure on Koepka, who drilled his drive straight down the middle of the fairway and safely found the green with his second before a cast-iron two-putt par completed his second 66 of the weekend for a winning score of 16 under par – lifting the 100th PGA Championship in his 100th start on the PGA Tour.
Stewart Cink enjoyed his first top 10 finish in a major since denying Tom Watson at The Open in 2009 as he birdied the final two holes to return a 67 and close on 11 under alongside Jon Rahm, whose slim hopes were ended by a bogey-six at the 17th.
Pieters looked certain to post a competitive score in the clubhouse when three consecutive birdies from the 14th got him to six under for the day and 12 under for the tournament, but he found water twice at the 17th and ran up a costly double-bogey seven.
The Belgian parred the last to settle for a 66 and a share of sixth with Molinari (67), Thomas (68) and halfway leader Gary Woodland (69), while Rafa Cabrera Bello and Tyrrell Hatton both fired sparkling 64s to complete the top-10 on nine under par.