Winning his first PGA Tour title, the 30-year-old Hoffman birdied No. 17, eagled the 18th in regulation, then birdied the 18th in the playoff.
He closed with a 1-under 71 to match Rollins (73) at 17 under.
Rollins' shot into a fairway bunker on the extra hole cost him.
Hoffman, in the next-to-last group, put the pressure on the final threesome when he hit his second shot within 11 feet of the pin on the par-5, 564-yard 18th, then rolled in the putt for an eagle to reach 17 under.
With Hoffman waiting and watching, Rollins, in the last threesome with Justin Rose and Lucas Glover, missed a long try for eagle but made the short birdie putt to force the playoff.
Rose, meanwhile, hit into a bunker off the tee on 18, then ran a long birdie try past the cup before sinking the par putt that left him at 16 under and a shot behind Hoffman and Rollins.
Rose, tied with Glover at the top heading into the final 18 holes, was shaky on the greens and finished with a 76 over the Classic Club layout.
Jeff Quinney, whose ace on the 176-yard 17th put him at 15 under, finished with a 73 to tie for fourth with Heath Slocum (72). Glover had an 80 that dropped him into a tie for 13th.