PHOENIX, February 3, 2014 (AFP) - Stadler's three-under effort gave him a 16-under total of 268 for the $6.2 million tournament on the TPC Scottsdale Stadium Course.
Stadler and 2012 Masters winner Watson were tied heading into the 72nd hole at 16-under par.
Stadler, the 33-year-old son of 1982 Masters champion Craig Stadler, found the fairway off the tee while Watson was in the right rough. From 122 yards out, Watson flew the green as Stadler landed his second shot 11 feet from the pin.
Stadler just missed his birdie putt and tapped in for par, but Watson, who chipped on, missed a five-footer and settled for a bogey and a share of second place.
"Obviously I would have liked to make that putt there and won it that way, but it's been a long time coming and I'll take it any way I can get it," Stadler said.
Watson finished with an even par 71 for 269. He was joined by Canada's DeLaet, who had seven birdies and one bogey in a 65 for his share of second.
Japan's Hideki Matsuyama and American Hunter Mahan shared fourth on 270. Matsuyama carded a 69 on Sunday and Mahan 68.
Stadler had five birdies to offset a double-bogey six at the par-four 11th. He admitted he had an erratic day, but was pleased to get a first US Tour victory under his belt.
"It wasn't pretty," said Stadler, whose previous biggest win was at the European Tour's 2006 Johnnie Walker Classic in Australia.
"I hit a lot of good shots and a lot of ugly shots, but it all worked out."
The Stadlers are the ninth father-son duo to win on the PGA Tour.
Watson went into the final round with a two-stroke lead, but Stadler erased that advantage with birdies from 10 and 26 feet at the first and second holes.
Watson and Stadler both birdied the third to stay tied, Watson edging back in front with a birdie at the par-three fourth where he landed his tee shot five feet from the pin.
Stadler jumped ahead at the ninth, dropping a four-foot birdie putt as Watson failed to get up and down from a greenside bunker for a bogey.
After an errant drive at 11 Stadler had to take an unplayable lie en route to his double-bogey that again saw him fall behind Watson.
Watson's bogey at 16 put them level again, and after both birdied 17 they went to the final hole tied.
Leading final-round scores on Sunday in the US PGA Tour $6.2 million Phoenix Open (USA unless noted. Par-71):
268 - Kevin Stadler 65-68-67-68
269 - Graham DeLaet (CAN) 67-72-65-65, Bubba Watson 64-66-68-71
270 - Hunter Mahan 66-71-65-68, Hideki Matsuyama (JPN) 66-67-68-69
271 - Charles Howell 70-69-67-65, Brendan Steele 66-74-62-69, Ryan Moore 66-71-64-70
272 Harris English 65-67-69-71
273 - Webb Simpson 68-72-67-66
274 - Pat Perez 65-68-70-71
275 - Cameron Tringale 71-67-69-68, John Mallinger 67-72-67-69, Matt Jones (AUS) 65-65-72-73
276 - Scott Piercy 67-67-75-67, Morgan Hoffmann 69-66-70-71, Greg Chalmers (AUS) 65-67-71-73, Jason Kokrak 66-69-68-73
277 - John Merrick 75-65-69-68, Michael Thompson 72-68-70-67, Kevin Na 70-70-68-69, William McGirt 65-69-73-70, Justin Hicks 71-70-69-67, Martin Laird (SCO) 67-68-71-71, John Rollins 72-67-67-71, Patrick Reed 67-67-71-72, Roberto Castro 72-69-70-66, Chris Stroud 70-67-68-72