Westwood's third shot on the extra hole found the water next to the green on the par-five 18th at the Wentworth Club, sealing the victory for Donald, who nailed down his fifth career European Tour win.
The victory will elevate Donald to the world's top spot for the first time. He completed the tournament at 6-under 278 after firing a 1-under 70 Sunday, garnering his ninth straight Top 10 finish.
Westwood had a chance to win but blew a two-shot lead down the stretch and wrapped up the fourth round at 3-under 68, matching Donald at minus-6.
Westwood missed a 6-foot birdie putt on the final regulation hole that would have earned him the title.
Simon Dyson (69) came in third at 4-under 280. He was followed by Marcus Fraser (67), Shane Lowry (67) and Raphael Jacquelin (71) in fourth at minus-2.