Westwood squandered a late two-shot lead and finished with a three-under 68 on Sunday to match Donald's minus-six. He bogeyed the 16th and missed a six-foot birdie putt on the 18th that would have given him the title in regulation.
After missing out on last week's chance to become No. 1 at the Volvo Match Play Championship, Donald didn't let another opportunity slip away.
Both Donald and Westwood headed back to the par-five 18th for the playoff, and while Donald drove into the fairway, Westwood hit it into the crowd well right, near a woman's backpack.
After the backpack was carefully removed, Donald's second left him with a pitch from the fairway, while Westwood was slightly closer to the putting surface. Donald's approach was spectacular, hitting it to the edge of the green and spinning it back to within five feet.
Westwood, meanwhile, spun it back into the water, all but ending his hopes. Donald, who was runner-up at this event a year ago, drained his birdie putt to claim the title.
"(No. 1) sounds pretty good, doesn't it?" Donald asked rhetorically on TV after he won. "It's an amazing accomplishment. It's something I'll be very proud of. There's more work to do, and there's more years of golf ahead of me."
Ahead by one, Westwood hit an errant tee shot on 15 into the crowd. He recovered with an unbelievable approach, allowing the green's slope to take the ball to within five feet of the pin.
Although Westwood gave himself some breathing room with a birdie on 15, he stumbled by three-putting on the 16th. His tee shot just missed the fairway bunker, and his first putt didn't break toward the hole. The bogey dropped him to six-under, still one shot ahead of Donald.
Donald, in the group behind, followed by drilling his approach to a foot on the 16th, leaving a tap-in for birdie to tie Westwood atop the leaderboard.
"To make birdie on 16, it was just a tense finish," Donald said on television. "I'm kind of at a loss for words. This is the flagship event for the European Tour...it means a lot."
With two par-fives to end the course, both players had good opportunities to make a move.
Westwood was unable to capitalize on the 17th, hitting his second well right of the green. He saved par from four feet to remain at six-under, and Donald's approach on 17 landed 12 feet from the pin. His birdie chance looked good the whole way until it lipped out at the very last moment.
On the 18th, Westwood hit his tee shot into the rough, but hit his second out into the fairway and third to within six feet of the hole. With a chance to put the pressure on Donald, however, his birdie putt stayed right the entire time.
Donald started the 18th with a disaster, hitting his tee shot into a fairway bunker. His blast out of the sand missed the fairway as well, but his third was well within two-putt distance on the green. He easily parred the hole to force a playoff for the No. 1 spot in the world.
Simon Dyson finished third at four-under 280 after firing a round of 69 on Sunday, while Marcus Fraser (67), Shane Lowry (67) and Raphael Jacquelin (71) shared fourth at minus-two.
Third-round co-leader Matteo Manassero struggled to a four-over 75 on Sunday and found himself tied for seventh at one-under with Colin Montgomerie (68), who recorded his first top-10 finish since 2008, Jamie Donaldson (69), Peter Whiteford (70), David Horsey (71) and Johan Edfors (71).
NOTES: Westwood notched his third straight top-10 finish...Donald is now 1-1 in playoffs in his career, while Westwood is 3-5...Next week is the Wales Open at The Celtic Manor Resort, site of the 2010 Ryder Cup. McDowell won that title before winning the U.S. Open and capping off his season with the decisive point at said Ryder Cup.