Hoffman finished regulation birdie-eagle to post a 1-under 71 and get into the clubhouse at 17-under-par 343. Rollins two-putted for birdie on the 90th hole to match Hoffman at minus-17 after a final-round 73.
Hoffman and Rollins returned to the 18th tee at The Classic Club for the playoff. Rollins found a fairway bunker off the tee before Hoffman bombed one down the middle of the fairway.
Rollins pitched out into the fairway with his second. Hoffman hit an 8-iron to about 35 feet. Rollins, who won for the second time on the PGA TOUR last year, followed by hitting his third some 33 feet from the hole.
Hoffman left his eagle putt 4 feet short, but watched as Rollins two-putted for par. Hoffman calmly knocked in the birdie effort for his first PGA TOUR title.
'I didn't really think I ever had a chance coming into 17,' said Hoffman, who earned $900,000 for the win. 'I just made a great bogey on 16 and made birdie, eagle to finish and somehow I got it done.'
This was the only five-round event on the PGA TOUR schedule. During this event, play rotated over four courses the first four rounds. Those courses were Bermuda Dunes Country Club, the Arnold Palmer Private Course at PGA West, La Quinta Country Club and The Classic Club, which hosted the final round.
Justin Rose, who shared the lead entering the final round with Lucas Glover, faltered to a 4-over 76. He finished alone in third at minus-16. Jeff Quinney, who aced the par-3 17th, tied for fourth with Heath Slocum at 15-under-par 345.
Glover closed with a birdie on the last, however he struggled to an 8-over 80 to end in a tie for 13th at minus-12.
Scores soared in the final round due to gusting winds. There were just three rounds in the 60s, while six players shot 80 or worse. Joe Ogilvie had the low round (68), while Dean Wilson's 84 was the highest of the day.
Rose was in control early after a birdie at the first put him two clear of the field. However, he double-bogeyed the fifth, then bogeyed seven and eight to tumble to 17 under par and into a share of the lead with Quinney.
Quinney had a double-bogey and three birdies on his front nine to turn at 17 under. He fell down the leaderboard with a double-bogey on 11. He dropped to 13 under after bogeys on 13 and 16, but got back into the mix with his hole- n-one at the 17th.
Rose's 7-foot birdie putt at 10 moved him back to 18 under, two clear of the field. He found water off the 11th tee for the second straight day and that led to a bogey. Rose came up short at the 13th and could not save par there either.
With that bogey, the Englishman slipped to 16 under and into a tie for the lead with Rollins. Rose parred out to come up one short. He did have a 22-foot putt for birdie at the last, but missed right of the cup.
Hoffman had two birdies and two bogeys on his front nine, and trailed by one as he made the turn. He dropped three back with a bogey on 11, where he also found water off the tee.
The 30-year-old was two behind the leaders after a bogey on 16. Hoffman fought back by sinking a 15-foot birdie putt on the 17th to move to 15 under and within one shot of Rose and Rollins.
Hoffman was in the left rough off the 18th tee, but knocked an 8-iron to 11 feet. He poured in that putt for an eagle, which gave him his first lead at 17 under.
'On 17, I pured my tee shot, then Quinney right behind me makes a one so I'm like 'well he jumped in front of me, so I need to make that just to stay up with him,'' Hoffman said.
'I didn't know what to hit off the 18th tee, but after Quinney hit 3-wood into the bunker, I hit driver and it almost went into the cross-bunker. I hit a good one in from there and made the putt, then got it done in the playoff.'
Rollins seemed to be out of the tournament with four bogeys in the first eight holes that dropped him 14 under. He got one stroke back with a birdie on nine and made it two straight with a birdie on 10.
The two-time winner on the PGA TOUR parred his next seven holes to hold steady at 16 under.
Rollins, playing in the final group, knew he needed birdie on 18 to force a playoff. He did just that as he two-putted for birdie from 26 feet to force the extra session.
'Obviously the wind howled all day and there was really no let up,' Rollins stated. 'I got off to a bad start, 4 over early. My caddie just kept trying to calm me down, telling me to stay with it and be patient.
'I righted the ship midway through the round and gave myself a chance coming in. I made some good putts to save pars to keep the momentum going, but just came up a little short in the playoff.'
Charles Warren and Cliff Kresge each closed with even-par 72s to share sixth place at 14-under-par 346. Scott Verplank, Robert Allenby, Mark Calcavecchia, Harrison Frazar and Dudley Hart were one stroke further back at minus-13.
Masters champion Phil Mickelson also struggled in the windy conditions. He closed with a 6-over 78 to share 45th at minus-7.