Allenby shot a 71 and Stenson 69 to tie at 11-under-par 71 in regulation play.
Each parred the first two holes of the playoff. On the third extra hole, Allenby hit his approach shot within 5 feet of the pin and won with two putts after Stenson missed a 30-foot par attempt.
"The only thing in my mind (on the third playoff hole) was hitting my 6-iron straight at the pin, and I hit it absolutely perfectly," Allenby said.
Tim Clark (69) and Ross Fisher (70) tied for third place at 278 and Retief Goosen, who led after three rounds, slipped to a 75 and finished fifth at 279.