Ames won with a par on the second playoff hole, posting his fourth PGA Tour win.
"At the end of the day yesterday, I said if I shot 64 I had a good chance at winning the tournament," Ames said.
Ames' 8-under-par final round left him tied with Leonard (67) and McNeill (67) at 18-under 270, setting up the playoff.
Leonard barely missed a putt that would have won the tournament on the final hole of regulation play, and then was eliminated on the first playoff hole.
On the second extra hole, Ames parred and McNeill missed a par putt of under 5 feet.
Nick O'Hern (67) and Justin Rose (68) shared fourth place at 271.
Ames won $846,000.
The tournament was the last of the season on the tour.