For the second week in a row, Trevor Immelman, who shared the 54-hole lead with Adam Scott, fell apart on the 72nd hole of the tournament.
On Sunday, he trailed Wetterich by a single stroke on the 72nd hole and Wetterich hit a strong drive down the fairway. Immelman, who struggled with his driver all day, mostly pushing it right, pulled this one into a lake.
After his drop, Immelman knocked his third to 7 feet to put the pressure on Wetterich to save par. Wetterich's pitching-wedge approach stopped 18 feet from the hole.
Wetterich only needed to two-putt for the victory and he lagged his birdie try into tap-in range. Immelman made the putt to complete the impressive par save and take second alone.
Then Wetterich became the fifth first-time winner this season on the PGA TOUR.
'This makes me feel really good,' said Wetterich, who pocketed $1,116,000 for the victory. 'To come out here and win this great golf tournament, it's just an unbelievable feeling. And being Mr. Nelson's tournament, also, it's truly an honor.'
Immelman managed an even-par 70 and despite back-to-back close calls on tour, he remains optimistic about win No. 1 on the PGA TOUR.
'Once I got in the hunt, I really didn't want to back off, continue to try and play my game,' said Immelman. 'I felt like I did that today. Once again, it wasn't quite my day. All credit to Brett. He played really solid down the stretch.'
Scott struggled to a 1-over 71 and tied for third place with Omar Uresti, a sponsor's exemption, who shot a 2-under 68 on Saturday. The pair finished at 10-under-par 270.
Chad Campbell carded a 1-under 69 and finished alone in fifth place at minus-9.
The lead was shared by several players on Sunday, but Immelman built a two-shot advantage around the turn. Immelman missed an 11-foot par putt at the 12th and suddenly there was a four-way tie for the lead between Charley Hoffman, Uresti, Immelman and Wetterich, who was even through 12 holes thanks to three birdies and three bogeys.
Hoffman fell quickly off the pace, leaving the other three tied at 10 under par. Both Immelman and Wetterich birdied the par-3 13th from inside 10 feet to move one clear of Uresti.
Wetterich continued to play smart golf, hitting fairways and greens. Immelman struggled with his driver and it burned him at the 15th. He missed the fairway, then missed the green with his second. Immelman chipped to 12 feet and failed to convert his par save, falling one behind Wetterich.
Both Wetterich and Immelman two-putted for birdie at 16, then both parred 17. Immelman needed either a birdie at the last, or a Wetterich bogey to have a chance at another playoff, but his driver and Wetterich's steadiness allowed Wetterich a spot in the winner's circle.
'I hit a lot of fairways today,' said Wetterich. 'I was just trying to stay in the moment and I thought I did a pretty good job of that. I stayed pretty patient and it turned around for me on the back nine today.'
Shigeki Maruyama (66), Luke Donald (68), Brian Davis (65), Rod Pampling (66), Jason Bohn (67), Dudley Hart (69) and Hoffman (71) shared eighth place at 7-under-par 273.
Ernie Els, the sixth-ranked player in the world, posted a 2-under 68 and moved into a tie for 13th place at minus-6.
Vijay Singh, No. 4 in the world, went the opposite direction on Sunday. He struggled to a 3-over 73 and tied for 48th place at even-par 280.