Earlier, Woodland carded a closing 64 to set the pace on 18-under-par 266, a total that was only matched by Reavie when he birdied the last to sign for a 66.
The duo finished three shots clear of countrymen Ollie Schniederjans and Brendan Steele.
Overnight leader Rickie Fowler faded with a 73 to tie for 11th, while Jon Rahm and Phil Mickelson, who like Reavie both played college golf in Arizona, also came up short in front of another raucous crowd at the biggest party on the PGA Tour.
The long-hitting Woodland credited his victory to an improved short game.
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"I put a lot of work in this off-season. Short game needed some adjustment," the 33-year-old said after clinching his third victory in 207 starts on the PGA Tour. "We're just building. I've still got some work to do but I'm excited where we're at."
Fowler's collapse, meanwhile, hardly dispelled his reputation as a player renowned for struggling to close out the deal, having now converted only one of six 54-hole leads on the PGA Tour into a victory.
The popular American was still in contention until late in the round, before three consecutive bogeys from the 15th ended his challenge.
Rahm started the final round one stroke off the lead but never quite recovered from a bogey at the first, shooting 72 to sit alongside Fowler at 12-under.
The Spanish world number two won the CareerBuilder Challenge two weeks ago but Sunday marked the second straight week that he has failed to deliver in the final round when sitting near the top of the leaderboard.
Mickelson, meanwhile, remains winless since the 2013 British Open. The five-times major winner made a late challenge with three successive birdies from the 15th, but a double-bogey at the last condemned him to a tie for fifth on 14-under.
(Reporting by Andrew Both in Adelaide, South Australia; Editing by John O'Brien)
