The 37-year-old Yang finished at 9-under 271 for his first victory on the PGA Tour.
Yang held a one-shot lead entering the final round and birdied three straight holes on the front nine, enough to hold off Rollins, who birdied four of five holes around the turn.
Rollins closed with a 67 for 272 and Ben Crane (68) was third at 274. Jeff Klauk (71) was another two strokes back in fourth place.
Yang joined K.J. Choi as the PGA Tour winners from South Korea.
"I'm just very happy right now for the way I played today," Yang said through a translator. "Before I went out this morning, my coach told me not to rush anything and keep your own routine, take it steady, and that's what I did today."