Woods, who has won his last five PGA TOUR starts, but lost two weeks ago in the European Tour's HSBC World Match Play Championship, drained a 20-foot eagle putt on the 18th to shoot 8-under-par 63 and lead by one stroke.
Stewart Cink and South African Ernie Els are tied for fourth place at 6-under-par 65. One stroke behind that duo is Jyoti Randhawa and Englishman David Howell, who trails Paul Casey on the European Tour's Order of Merit.
Woods wasted no time in climbing the leaderboard. After a birdie on the par-5 second, he drained a 24-footer for birdie at the third. He stuck his approach shot 3 feet from the hole at the fifth and kicked in the birdie effort.
Heading to the seventh tee, Woods was two behind Harrington and Howell. That quickly changed.
Woods chipped in from just off the green at the par-3 seventh, then sank an 11-footer for birdie on eight. He made it three straight when he tapped in a 4-footer for birdie on nine.
Making the turn at 6 under par with a one-stroke lead, Woods cooled with five straight pars at The Grove. As he parred those five, Woods was joined in the lead by Harrington and Cink.
Woods, the defending champion, responded with an up-and-down birdie on the par-5 15th to again take the lead by himself. However, Woods knocked his second shot over the green at the 17th and was unable to save par from 45 feet. He went to the 18th one shot behind Harrington.
'That bogey wasn't very good with a wedge in my hand,' admitted Woods of his approach on 17.
The 30-year-old Woods found the fairway off the tee at the last. From just under 270 yards out, he hit a 3-wood to 20 feet. Woods calmly ran that putt in to take the overnight lead.
'I hit two good shots on 18 and I gave myself a chance at a three and somehow it found the bottom,' said Woods of his putt on 18. 'That was about as far as my 3-wood was going, especially into the wind. I absolutely tattooed that one, which was nice.'
The field better be on top of their collective games the rest of week as Woods has won 11-of-21 World Golf Championships he has played in.
Harrington, playing three groups ahead of Woods, got off to an equally solid start. He birdied three of the first four holes, then converted a 9-foot birdie putt on the fifth to move atop the leaderboard at minus-4.
The Irishman parred six and was tied for the lead with Cink and Howell. Harrington responded with a 7-foot birdie putt on seven to retake the top spot.
Harrington parred seven consecutive holes from the eighth. He two-putted for birdie on the par-5 15th, then sank a 16-footer for birdie on 18 to end at minus-7.
'I birdied four of the first five, the first two were pretty easy. Then I holed that long one, about 40 feet, at the fourth, so making birdie on that tough par-3 was a bonus,' admitted Harrington. 'After making a 9-footer on the fifth, all of a sudden I'm thinking I can shoot 59. The beauty of this golf course is that you feel you can hole a putt from anywhere.'
Poulter started on the back nine and picked up a birdie on the 10th. After giving that stroke back with a bogey on No. 12, he converted birdies on 13 and 14. Poulter dropped another stroke on the 15th, however.
The Englishman made the turn at 2 under thanks to a birdie putt on the 17th. Poulter poured in back-to-back birdies from the first, then got to minus-5 with a birdie on five. Poulter birdied the seventh, then sank an 18-footer for birdie at the last to share second.
Ryder Cuppers Chad Campbell, Jim Furyk and Robert Karlsson each opened with rounds of 4-under-par 67. They share eighth place with Adam Scott, Simon Dyson and Nick O'Hern.
Darren Clarke and Luke Donald, who combined to go 6-0 for the European Ryder Cup team last week, are one stroke further back at minus-3. They stand alongside Henrik Stenson, Tim Clark and Trevor Immelman.