In the playoff, which was held on the par-4 18th hole, Johnson knocked a shot from a fairway bunker to within a foot of the hole. After Matteson missed his 20-foot birdie try, Johnson tapped in his birdie for his ninth career win the PGA Tour, and second this year.
Johnson and Matteson had made double bogeys after going in the water the first time they played No. 18 in the playoff.
Johnson started the day four shots behind Matteson, the third-round leader.