Haas closed with a 3-under 68, while Bryant finished eagle-par-birdie to post even-par 71 and join Haas in the playoff at 5-under-par 279.
'It's pretty neat stuff to finally win a major,' said Haas, who earned $360,000 for the win. 'I feel bad for Brad. He played a lot of good shots.'
The par-4 18th played as the first extra hole and it saw Haas two-putt from 45 feet for par. Bryant's approach got hung up in the wind and came up short of the green. He got up and down for his par, though.
The duo moved to the par-4 first for the second playoff hole. Haas missed the fairway well right, then came up short of the green with his second shot. Bryant got a lucky kick as his tee shot ricocheted back into the fairway.
Haas chipped inside two feet and tapped in for par. Bryant left himself 12 feet for birdie, but he left that effort short and it was back to No. 18.
'I felt it was going to be over on the second playoff hole,' Haas admitted. 'I was trying to figure out what I would say to Brad after it went in. It looked like his day after he made that long putt on the last hole to tie me. I felt like he was going to make that one.'
Haas lost his approach to the third extra hole in a deep bunker right of the putting surface. Bryant then knocked his second shot to the back edge of the green, leaving himself a long and difficult birdie try.
Bryant's birdie putt came to rest 5 feet left of the hole. Haas blasted out of the bunker to 15 feet. He rolled the improbable par putt into the cup and when Bryant's par putt slid by the left edge, Haas had claimed the first major title of his career and third win this season.
'I hit every putt I had today like that, just exactly like that - weak and left,' admitted Bryant. 'Gosh I was lucky to be in the playoff. Let's face it, I played great coming down the last few holes, but early in the round I really stunk the place up. Second place in a major isn't bad.'
Gil Morgan, the third-round leader, closed with a 3-over 74 to end alone in third at 3-under-par 281. He was one ahead of Bryant and four clear of Haas to start the day.
Dana Quigley posted an even-par 71 to end at minus-2 and alone in fourth place. Loren Roberts was one stroke further back at 1-under-par 283 after a final-round 73. Tsuneyuki Nakajima ended alone in sixth at even-par as he carded a 2-under 69 in the final round.
Haas looked to be out of the picture early on. He bogeyed the second and third to fall to even-par for the championship. Bryant, playing one group behind Haas, birdied the second to get to minus-6.
The 52-year-old Haas flew back into the mix as he caught fire from the fourth. He birdied the fourth and fifth from just outside 10 feet to get back to minus-2.
Haas kicked in a 3-footer for birdie on six, then sank a 6-foot birdie try at seven. He capped a run of five straight birdies by making a 5-foot putt on the eighth to join Morgan in the lead at 5 under.
Meanwhile, Bryant was struggling to stay in the mix. He bogeyed the fifth and sixth, then stumbled to a double bogey at the seventh. He stood at minus-2, but was able to get one stroke back with a birdie on eight.
Bryant hit into the trees left of the fairway at nine and pitched out. He was unable to save his par there and dropped back to minus-2, three behind Haas.
Haas turned at minus-5 and seemed to be in control. He was playing conservatively on the back nine and it cost him as he three-putted for bogey at the 12th.
Standing at 4 under, two clear of the field, Haas parred his next five holes. He was lucky to par the par-5 16th as his second shot hit a wood piling bordering a hazard and kicked his ball into play instead of into the hazard.
He pitched to 9 feet from there, but left the birdie try shy. Haas drained a 15-footer for birdie at the 18th to get back to minus-5.
'Six-under was my number I felt like I needed to get to,' Haas stated. 'I was not trying to play safe. I hit a lot of good shots on the back nine. My putting touch just left me a little bit. I was fortunate to make par at 16 and the birdie putt at 18 was pretty sweet.'
Bryant dropped four behind Haas at 1 under par as he bogeyed the 11th. He climbed within one of Haas' lead with back-to-back birdies from the 13th.
After a bogey on 15, Bryant's second shot to the par-5 16th stopped 5 feet from the cup. He sank the putt for eagle and a share of the lead. After a par on 17, Bryant drained a 25-foot birdie putt to join Haas at minus-5.
Katsuysohi Tomori fired a 4-under 67 in the final round to end at 1-over- par 285, where he was joined by second-round leader Peter Jacobsen (75). Doug Tewell took ninth place at plus-3, while D.A. Weibring was one stroke further back at 4-over-par 288.