Els, who cruised to a less stressful five-shot victory here last season, collected the whopping $2 million first-place check for his trouble this year.
Els and Westwood began the playoff on the par-3 16th after finishing 72 holes tied at 20-under-par 268. They traded pars then moved on to 17, where they each hit their approaches to within birdie distance.
But while Westwood narrowly missed with his seven-foot try, Els managed to roll in his four-footer for the win.
Els, who shared a two-shot lead with Denmark's Thomas Bjorn after three rounds, bogeyed the first hole and would soon find himself looking up the leaderboard at Nick Price, who birdied five of the first 10 holes Sunday to take the lead at 19-under.
Price cooled off, however, logging eight straight pars to close with a 67. Price, the winner of this event in 1993, '97 and '98, tied for third with Bjorn, who turned in a final-round 69.
Els finally made it to 19-under with his fourth birdie of the day at 16, but now Westwood had the lead. Earlier, Westwood holed out his bunker shot at the 13th for the first of three straight birdies that took him to 20-under.
Els went on to birdie 17, and with Westwood in the clubhouse with the day's low round of 6-under 66, needed to birdie the final hole to win in regulation. His approach to the 18th left him with a 30-foot putt for birdie, but his attempt curled away at the last second.
Els closed with a 4-under 68.
John Huston, the lone American in the 12-man field, shot 71 on Sunday to take fifth place at 14-under-par, while Scotland's Colin Montgomerie finished in sixth at 12-under after carding a 69.
Spain's Jose Maria Olazabal, the co-leader with Westwood following Thursday's opening round, finished at 11-under, three shots ahead of Michael Campbell of New Zealand and Australian Stuart Appleby.
Paraguay's Carlos Franco was next at minus-seven. Darren Clarke of Northern Ireland ended the event at 4-under-par and Spain's Miguel Angel Jimenez finished at Even-par 288.