Bob Tway and Geoff Ogilvy tied for third at 13-under, while overnight leader Mark Wiebe, looking for his first win in 14 years, struggled to a two-over 74 and finished three shots off the pace at minus-12.
Wiebe was in control of the tournament until early on the back nine. He bogeyed 11 and followed with another bogey at 12. That bogey, coupled with a birdie by Willis on the same hole, gave Willis a one- shot lead at minus-15.
While Wiebe continued his descent down the leaderboard, Sutherland was moving up at the same time. He birdied 13, 15 and 16 to get to within one of Willis' lead. At the par-three 17th, Sutherland hit a beautiful approach shot that landed five feet from the stick. He pulled the putt left and was forced to take par heading to the difficult 18th.
Sutherland hit his tee shot down the middle at the closing hole, but his approach shot landed some 60 feet right of the hole. He two- putted for par and kept the pressure on Willis.
Willis had plenty of opportunities at the end of the round to extend his lead. At the par-five 15th, he played his third shot from a fairway bunker onto the green about 25 feet short. Willis was putting for a two-shot lead, but missed the putt left.
At 16, Willis was short on a 20-foot birdie effort. He then hit his tee shot at 17 directly over the flag and watched as the ball rolled down the hill and stopped four feet from the hole. His birdie putt lipped out right and he carried a one-shot edge to the 18th tee.
The 465-yard 18th, with water right and left on the tee shot and a difficult left pin position, proved difficult for players before the final group as there were several double-bogeys and one triple. Willis used driver from the tee and played the ball down the middle of the fairway. He had 191 yards to the flag and left his ball 45 feet to the right and short on the fringe.
Willis had the luxury of being able to two-putt for the championship, but he took a run at the birdie, leaving himself about three feet coming back. He drilled the par save and won his first title.
'This is well beyond my means,' said Willis, who pocketed $540,000 for the win. 'A month ago, I was at qualifying school not knowing where I was going to play this year. Now, I'm a PGA Tour champion. This is a great country.'
Willis started Monday's final round two strokes behind Wiebe. His round got off to a shaky start with a bogey at number-two after an errant tee shot. The 27-year-old rebounded with a tap-in birdie at the par-three fourth.
The birdie at four was the first of three in a row. Willis added another birdie at number-eight, but lost a stroke at nine.
Willis joins Gamez in an elite group of golfers to win their first start on Tour. Gamez did it in 1990 at this event. Prior to Gamez, the last player to do it was Ben Crenshaw in 1973.
Sutherland, a first-round co-leader, finished the day with a four-under 68. He birdied his first two holes but bogeyed the third. Sutherland birdied the ninth before picking up his three back-nine birdies.
'I hit the ball very well today,' noted Sutherland, who was seeded 62nd in last week's Match Play Championship. 'I had a lot of opportunities to make birdies. I have no complaints today.'
Tway fired a six-under 66 on Monday to jump into a tie for third with Ogilvy, a first-round co-leader. The pair finished at 13-under for the tournament.
Cliff Kresge, K.J. Choi and Greg Kraft joined Wiebe in a tie for fifth at minus-12. Kresge and Choi posted 66s, while Kraft carded a 68.
The tournament was completed on Monday due to snow and rain in the Tucson area on Friday, which caused the second round to be postponed for the day.
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