Darren Clarke opened with a 7-under-par 64 and owns a two-shot lead after rainy conditions at the Phoenix Country Club.
Clarke, who represented Europe in the Ryder Cup two months ago, collected six birdies on the front nine. He dropped a shot with a bogey at No. 16 but rebounded with birdies at 17 and 18 for his 64.
'The changes they've made to this course make it a lot more tricky,' said Clarke. 'But I putted as well as I have in years and got a couple of breaks that I made the most of.'
Woods opened on No. 10 Thursday and struggled out of the gate. He three-putted the 12th for bogey and drove left at 13 and failed to save par. He birdied 16 and 17 to draw back to even-par, but there was trouble looming after the turn.
Woods dropped another shot at the second when he failed to get up and down for par from a greenside bunker. He bogeyed the third but birdied four and seven to get back to even-par.
'To shoot even-par is a mini-miracle,' said Woods. 'I didn't hit it well and didn't putt well, but managed to salvage the round with a couple of birdies near the end.'
England's Justin Rose, Japan's Kaname Yokoo and Tsukasa Watanabe opened with 66s, while Sergio Garcia of Spain headlined a five-player group at 67.
David Duval, the 2001 champion, posted a 69 on Thursday based on six birdies, two bogeys and a double bogey.
'I hit it all over the place today,' Duval said. 'But 2-under with three unplayables is pretty good. It was cold out there and it's always hard to get warmed up in those conditions.'
Full-Field scores for the Dunlop Phoenix Open