It was the second PGA Tour win and 12th on the European Tour for Poulter. He collected $1.2 million for the championship.
His score was two clear of a group of four player who tied for second. Jason Dufner turned in an 8-under 64 while Scott Piercy matched Poulter's 65, Ernie Els shot 67 and Phil Mickelson 68 in ending the tournament at 19-under.
Oosthuizen and Westwood each shot even-par 72 and slipped into a tie for sixth at 18-under 270.
Four times Sunday Poulter posted back-to-back birdies. He had birdies at Nos. 2 and 3 and again the seventh and eighth. After a par at the ninth, Poulter tied for the lead with a birdie at 10 and knocked in a 3-foot birdie putt at 11 for the outright lead.
Birdies at 14 and 15 -- where he made a sand save for a 4 on the par-5 hole -- pushed the lead to three strokes. He had a bogey at 17 but no one could catch him.