The world number three, U.S. PGA champion at Sahalee in 1998, holed a 10-foot birdie putt at the par-four 10th, the first of three extra holes, before edging out Americans Justin Leonard and Chris DiMarco for the prized Wannamaker Trophy.
Singh then parred the next two holes -- 17 and 18 -- to secure his fifth PGA Tour victory of the year.
The trio had completed a tough final round at Whistling Straits level on eight-under-par 280, Singh carding a 76, Leonard a 75 and DiMarco a 71.
The Fijian, winner of the 2000 U.S. Masters, had led by a shot going into the last day but appeared to throw away his victory hopes when he double-bogeyed the fourth and then dropped on seven and 15.
But Leonard, who had been one clear with three to play in regulation, bogeyed three of the last five holes to take the tournament into a playoff.
Three-times major winner Ernie Els returned a 73 to tie for fourth at seven-under 281 with American Chris Riley, also after a 73.
U.S. Masters champion Phil Mickelson closed with a 74 to share sixth place with Ireland's Paul McGinley (69) and South Korea's K.J. Chi (70).
Leonard, the 1997 British Open champion, had caught Singh at the 181-yard third, where he holed a 15-foot birdie putt.
The 32-year-old Texan then moved clear at the par-four fourth where Singh ran up a double-bogey six after pulling his tee shot into a bunker in the left rough before finding sand with his second shot.
Leonard, ice-cool as the wind began to pick up, scrambled well to save par on five and six before he missed a short putt for par at the seventh to slip back to 11 under.
He then parred the next two holes to take a two-shot cushion into the tough closing stretch.
But DiMarco, who had picked up his first shot of the day at the par-four ninth, reeled off further birdies on 11 and 12 to move to 10 under.
Moments later, Leonard bogeyed the par-four 10th after overshooting the elevated green with his approach and failing to get up and down. He was now locked in a tie for the lead with DiMarco with eight holes remaining.
Leonard had a chance to move ahead at the monster 618-yard 11th, but missed a birdie putt from eight feet.
However, he holed a 20-footer for birdie on 13 to go two shots clear of the chasing pack before dropping his third shot of the day at the par-four 14th before his stumbling finish.
The par-72 Straits Course, already the longest layout in major championship history, had been stretched to 7,526 yards for the final round, with pin positions at their most difficult for the week.
World number one Tiger Woods was one of several players to struggle, mixing five bogeys with four birdies on his way to a one-over-par 73.
Woods, who has not won a major since the 2002 U.S. Open, finished at two-under 286.
"It's very disappointing," said the 28-year-old. "I felt like I was playing quite well going into the tournament, but I just didn't put it together on the first day."