Haas closed with a 5-under 67 for his sixth PGA Tour title and first since the 2013 AT&T National. He won the 2010 event at PGA West for his first tour victory.
Haas was making his first start since November. He took the long break to rest his left wrist, fractured in April when he fell down stairs at Hilton Head.
Part of a six-man tie for the lead after a par save on the par-3 15th, Haas got to 22 under with the birdie putt on 16 on the Arnold Palmer Private Course.
Haas two-putted for par from 20 feet on the par-5 18th after pulling off an awkward layup with his ball perched on the front lip of a right-side fairway bunker.
His father, Jay, won the 1998 tournament. Haas' great uncle, 85-year-old Bob Goalby, watched the final holes. Goalby won the 1968 Masters.
Kuchar had a two-stroke lead with four holes to play Saturday, but bogeyed three of the last four holes in the third round to fall a stroke back.
Haas eagled the par-5 sixth for a share of the lead, setting up his 15-foot putt with a 260-yard, 5-wood from the dormant left rough with the ball below his feet.
The 32-year-old former Wake Forest player birdied the par-4 eighth, punching a low, spinning wedge from 70 yards to 8 feet, and got to 21 under with a 7-foot birdie putt on the par-5 11th.
He made a key par save on the 131-yard 15th to keep a share of the lead. Short-sided in the left bunker, he blasted to 6 feet.
Haas broke out of the tie on 16, and then missed a 10-foot birdie try on the par-3 17th with a bighorn sheep grazing nearby at the foot of the Santa Rosa Mountains.
On the par-5 18th, with water running the length of the hole on the left, his drive stopped on the top edge off the right-side bunker. Standing in the bunker with the ball in the dormant grass at nearly waist level, he choked up on an 8-iron and slashed 80 yards down the fairway. That left him 170 yards to the green and he hit safely to the middle.
Thomas, playing alongside Haas and two-time heart transplant recipient Erik Compton in the final group, dropped out of the lead on 16 with a double bogey after hitting his approach from a bunker into the All-American Canal. The 21-year-old former Alabama player birdied 18 for a 69.
Simpson finished with a 64, and Weekley shot 65.
Compton had a 70 to tie for 10th, three strokes back at 19 under.
DIVOTS: Colt Knost had a 63 - the best round of the day - to finish in the tie for 10th at 19 under. He was in the first group off the 10th tee and played his final nine holes behind Haas' group. ... Patrick Reed, the winner last year, shot a 71 to join Mickelson in the group at 15 under. He started the year in Hawaii with a playoff victory in the Tournament of Champions.