Harrington and Woods closed with rounds of 3-under 67 to finish at 9-under-par 271, one stroke clear of Keiichiro Fukabori.
Woods, who had won this event the last two years, pulled away from the Irishman early on. Woods birdied the second, but gave that stroke back with a bogey on three at Phoenix Country Club.
The world's No. 1 player responded with birdies on four and five, while Harrington bogeyed the fourth to give Woods a three-stroke cushion. Each man birdied the 11th, and that got Harrington going.
The Irishman came back with a birdie on 13 to get within two. That gap was gone when Woods three-putted for bogey on the 16th and Harrington birdied the same hole. They both parred the 17th setting a dramatic final hole.
Harrington found the rough off the tee and had to thread his second through the trees. He did that with no problem setting up a birdie. Woods also birdied the last to create the two-man playoff.
Fukabori took third place at minus-8 thanks to a final-round, 6-under 64. Justin Rose and Shingo Katayama were one stroke further back at 7-under-par 274.
Ian Poulter used a 5-under 65 to match Toru Taniguchi at 4-under-par 276 in a share of sixth. Gonzalo-Fernandez Castano and Takuya Taniguchi tied for eighth at minus-2, while Hisayuki Sasaki and Yusaku Miyazato shared 10th place at 1-under-par 279.