Haas also won the $10 million prize for finishing first in the race for the FedExCup.
Both players got up and down for par on the first extra hole, No. 18.
They headed back to the 17th, and Haas found a fairway bunker, then pulled his approach left of the green. His ball came to rest on the edge of a pond.
Mahan, from the fairway, dropped his approach 25 feet from the hole.
Haas hit a spectacular shot out of the water to two feet, and Mahan missed his birdie effort on the left. After both players tapped in for par, it was back to the 18th for the third playoff hole.
"The second shot, I actually thought I hit a pretty decent shot, just pulled it a little bit, which might have made it go a little further. I got an unbelievably fortunate break to basically just have a bunker shot down there in the water," Haas explained in a television interview.
"It was all or nothing there. Hunter is going to make it or two-putt, so I had to hit a decent shot. There was some luck involved because it had some spin on it. That was very lucky."
Mahan was impressed too.
"There was quite a bit of room there. His ball was maybe half in," Mahan said on TV. "I mean, he spun it. That's all you need to know. It was a beautiful shot. He sucked it a little bit, it was pretty impressive"
Haas, who had missed the green right in regulation and on the first extra hole, found the back fringe with his tee ball. Mahan then dumped his tee shot into a right greenside bunker.
Mahan blasted to 15 feet and onto a similar line to what Haas had. Haas' birdie try from the fringe rolled past the left edge and four feet by the hole, and Mahan's par effort missed badly to the right.
Haas, who started the week 25th on the FedExCup points list, stepped up and drained the winning putt.
"Being that I was 25th, all I could do was win, then hope. Everything fell into place, I got lucky," Haas stated in a televised interview. "Webb Simpson has played the best golf of anybody here in the Playoffs. It just worked out for me."
Haas closed with a two-under 68 and Mahan posted a one-over 71. They finished at eight-under-par 272.
The two big prizes might not be the only things Haas won on Sunday. He finished 12th on the Presidents Cup points list and was hoping to gain a spot via a captain's pick.
One more thing on Haas' side: his father, Jay, is one of Couples' assistant captains.
The battle for the FedExCup title was so tight that with the last group of Mahan and Baddeley on the final hole of regulation, there were still four players alive for winning the $10 million prize.
Once Haas and Mahan went to extra holes, whichever player won was going to claim both prizes, and Haas walked away the champion.
"I just hung in there. Very fortunate, this was pretty unexpected," said Haas on TV. "I'm very happy."
If Baddeley had birdied the final hole of regulation, then went on to win the title, Simpson would have claimed the FedExCup. Simpson didn't help himself on Sunday, closing with a three-over 73 to end in 22nd at plus-two. He finished second to Haas in the FedExCup standings.
Haas opened with a birdie on the first, but gave that stroke back on No. 3. Birdies on the sixth and ninth got him to minus-eight, where he was one back.
As Mahan and Baddeley fell backwards, Haas jumped into the lead at 10-under with birdies on 13 and 15. Haas, who dropped three strokes over the final two holes in the third round, lost his two-stroke lead on Sunday with bogeys on 16 and 18. However, he redeemed himself in the playoff.
Mahan, who slipped to a bogey on 13, birdied the 15th to get back to minus- eight. He parred out to join Haas in the playoff.
NOTES: The win was Haas' third on the PGA Tour...With his share of third place, Donald moved atop the PGA Tour money list. He leads Simpson by just under $69,000, and has a chance to become the first player to top both the PGA Tour and European Tour money lists in the same season...He leads the European Tour money list by more than 1.6 million Euros...The PGA Tour will be in Las Vegas next week for the Justin Timberlake Shriners Hospitals For Children Open, where Jonathan Byrd won last year with a hole-in-one in a playoff.