Rollins mixed his over-par holes with three birdies and an eagle and came away with an even-par round of 72, and a somewhat more-impressive 17-under 271 for the tournament.
"It was kind of an up and down day," Rollins said after notching his third career PGA win.
Rollins led by four strokes heading into Sunday's final round and promptly birdied the second hole at Montreux Golf and Country Club. A missed chip shot and two-putt on the par-5 fourth hole knocked him back to 16-under.
Rollins made up for the stumble by chipping in an eagle on the par-5 11th to move to 19-under and six shots ahead of the field. His lead was cut to two strokes on the back nine but a birdie on 17 restored it to three.