The British world No. 3 calmly drained a five-foot birdie putt at the fourth extra hole at the TPC Southwind to edge out Swede Robert Karlsson, who had been seeking a maiden win on the US circuit.
The Englishman threw his putter to the ground as his ball disappeared into the heart of the cup before he pumped his right fist in celebration.
It was Westwood’s first victory in the US since the 1998 New Orleans Classic and his fifth top-10 in just eight PGA Tour starts this season, including a runner-up spot behind Phil Mickelson at the US Masters in April.
“Just shows you, don’t expect nothing in this game because you never know what’s going to happen next,” Westwood, a winner of 20 titles on the European Tour, told reporters.
“Twelve years ago I won my first (US) tournament in New Orleans. I’ve won 25 more times since then, maybe more. Lost count. I’ve been in contention a lot, especially this year, and I suppose I got a break today with other people’s misfortune.”
Garrigus was desperately unfortunate to exit the playoff after bogeying the first extra hole where a booming three-wood off the tee ended up behind a tree from where he had to chip out sideways on to the fairway.
The trio had finished the 72 regulation holes on 10-under-par 270. Westwood closed with a two-under 68, Karlsson a 69 and overnight leader Garrigus, three ahead playing the last, triple-bogeyed the 18th for a 71 after hitting his tee shot into water.
“I handled everything great today except for one swing,” Garrigus said. “I’m glad I even got into the playoff. It’s just little things you do to win and I gotta learn that. Next time I’m in that position, I’m going to do it.”
For much of a hot and humid afternoon at Southwind, the tournament appeared to come down to a head-to-head duel between Westwood and Garrigus.
The American, two ahead of the chasing pack going into the final round, made a shaky start by bogeying the first and sixth holes to trail the experienced Englishman by two.
Westwood, in contrast, reeled off three consecutive birdies from the second to grab the outright lead but was unable to pick up any further shots for the rest of the round.
Garrigus birdied the eighth to reach the turn in one-over 36 and he then drew level with Westwood at the top when he rolled in a 10-footer at the par-four 10th.
Further birdies followed at the 15th and 16th, the second of them an 11-footer which prompted Garrigus to pump his right fist in jubilation as he moved two ahead.
Moments later, the American was three strokes clear after Westwood bogeyed the 17th, having found the right rough off the tee and taken another three shots to reach the green.
With his maiden tour victory firmly within his grasp, Garrigus succumbed to the pressure on the 18th tee.
He pulled his drive into water, took a penalty drop and then pulled his third shot low and well left into trees. From there, he punched out into the fairway, hit his fifth on to the green and two-putted for a triple-bogey seven.
“It was just a mess,” Garrigus said of his tee shot. “I wasn’t committed to the shot. I wanted to hit a high cut, and I just flipped it right into the water.”
