After both players parred the first playoff hole, Faxon had a chance to win at the second but missed a five-foot birdie putt. The advantage seemed to be with Tway as he hit his approach 18 feet from the pin, but Faxon blasted out of a fairway bunker.
The duo returned to the par-4 18th for the third playoff hole. Tway put his third shot on the green and two-putted for a bogey and his eighth career win.
Tway and Faxon finished 72 holes at 8-under-par 272. Tway fired his second straight 4-under 66 while Faxon had a 67.
The 44-year old earned $756,000, his largest paycheck in nearly 23 years on the PGA Tour.
Swim Week Miami Beach 2014 [PHOTOS]