Donald used a great approach shot on the extra hole to edge third-round co-leader Jim Furyk, Sang-Moon Bae and Robert Garrigus, and claim his fifth career PGA Tour victory. He dislodged Rory McIlroy from the world No. 1 ranking in the process.
Britain's Donald had surrendered the title only two weeks ago when the Northern Irishman won the Honda Classic.
Donald fired a 5-under-par 66 to finish at 13-under 271. Garrigus, meanwhile, had carded a 64, while Bae registered a 3-under 68 and Furyk settled for a 69 after missing a birdie on the final regulation hole.
Ernie Els (67) blew a chance to join the playoff when he missed a 4-foot putt for birdie at the 16th.