Koepka earned his third major title and second of 2018 by finishing 16 under at Bellerive Country Club in St Louis on Sunday.
The 28-year-old – who entered the final round with a two-shot lead – carded a four-under-par 66 to celebrate further major success, having already successfully defended his U.S. Open crown.
Despite two early bogeys, Koepka was able to hold off former world number one Woods and Australian Adam Scott to hoist the Wanamaker Trophy.
American great Woods finished second at 14 under after an impressive birdie on the 72nd hole, having flirted with victory.
The 14-time major champion, who has overcome serious back problems, fought hard all day, firing a final-round 64 to record his best finish in a major since 2009.
Woods started the week with a bogey and a double-bogey, but electrified the St Louis crowds with a valiant charge afterward.
The 42-year-old’s 196 (66-66-64) over the last three rounds marked his lowest score across 54 holes of a major in his career by four shots.
Birdies on 12, 13 and 15 gave Woods – chasing Jack Nicklaus’ record of 18 majors – a chance to win, but he hit his tee shot in the water on the par-five 17th to end his chance.
Scott, playing with a heavy heart after his fellow Australian Jarrod Lyle died following a cancer battle this week, finished three shots behind in third via a 67 on Sunday.
The former world number one, who won the 2013 Masters, actually had two putters in his bag during the final round.
Stewart Cink (67) and Spanish star Jon Rahm (68) finished tied for fourth at 11 under.
Defending champion and Justin Thomas led a group – including Francesco Molinari (67), Thomas Pieters (66) and Gary Woodland (69) – tied for sixth at 10 under.
Thomas came out firing, birdieing five of his first 11 holes, but two late bogeys ended his momentum.
Jordan Spieth, who was trying to complete his career Grand Slam, shot a four-under 66 to finish eight shots off the pace.
A three-time major champion, Spieth still does not have a top-two finish this season.
Rickie Fowler (71) was also eight under for the tournament, a stroke ahead of Justin Rose (68) and Jason Day (71), while world number one Dustin Johnson slipped to six under following his 69.
An even-par 70 saw Northern Irish star Rory McIlroy finish tied for 50th at two under.
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