Harrington only carded a 1-under 71 in the final round but his 20-under-par 268 was enough to hold off the hard-charging Woods.
It looked like Harrington blew his enormous lead when he hit an awful approach at the 14th that went out of bounds. He double bogeyed the hole but still went to the winner's circle, thanks to a collapse by the normally unflappable Woods.
Woods pulled his approach at the 16th that left him in a spot where he couldn't even take a backswing. He somehow chipped in for par at that hole but he didn't survive 18 when his approach left him in a hazard and ended his chances of a successful title defense.
'Most of the day went as expected,' said Harrington, who walked off with the $1 million first-place check. 'Tiger, I knew would come at me. He kept going and kept going and he really didn't relent.'
Harrington owned a two-shot lead after a course-record 63 on Saturday and he wasted little time before he extended his lead. He birdied the first two holes in Sunday's final round to push his lead to eight, but even that margin was almost too small for the Irishman.
Woods cut the lead to five around the turn and after a birdie at No. 10, Woods found himself only four down. Harrington hit a tree at the par-5 11th and bogeyed the hole to put the difference between Harrington and Woods at three.
But it was the 14th hole where the tournament got very interesting.
Woods made a routine par at the same hole but now his deficit was only one.
'I knew I was still ahead. I knew I was in still in control,' said Harrington. 'I kind of hit the shot without thinking too much about it. I got the wrong club. It was a mental error rather than a swing error so I was reasonably confident that I could keep going afterwards.'
The pair made pars at the downhill par-3 15th, but 16 provided another wild moment in this tournament.
At the par-5 16th, Harrington had 270 yards to the pin and landed his ball 35 feet short of the stick. Woods struck one of the worst shots of his career as he pulled a 3-iron into a thicket 40 yards left of the green.
Woods hit a provisional in case he was unable to find his ball but it was located on a hill, tangled in some branches. Woods muscled his third out of the trees but found some more trouble as his ball was now under a tree with a twig possibly interfering in his swing.
The top-ranked player in the game chipped his fourth through the green and into rough past the putting surface. Woods had his caddie pull the pin and then holed the chip for an amazing par-5.
After a smile when Woods chipped, Harrington still had 35 feet for eagle but missed his putt two feet short. He tapped in for birdie to gain a two-shot edge with two holes left in the final round.
Harrington found the left corner of the green at the par-3 17th but had close to 40 feet to the hole. Woods hit a 9-iron short of the green at the 158-yard hole but got a fortuitous bounce that left the ball eight feet from the cup and with a very makable birdie try.
The Irishman missed his birdie chance but Woods drained his to get within one shot of the lead one hole after the near disaster at 16.
Woods and Harrington both hit irons off the tee at Sherwood's difficult closing hole and both landed in the fairway. Harrington played first and applied the pressure to Woods with an approach that landed comfortably inside 20 feet. Woods pushed his second right of the green and into a hazard.
Woods pitched his third out of the hazard but was still farther than Harrington. Woods' par putt died short of the hole and gave the tournament host his first bogey of the round.
Harrington had three putts to win the title but nestled his birdie opportunity to tap-in range and won for the third time since the Ryder Cup in September.
Harrington won the Dunhill Links Championship in October and the Asian Open two weeks ago, which is the first tournament of the 2003 European tour schedule.
'I count it,' Harrington said. 'Against Tiger? Yes. Against a world-class field? Yes.'
Woods finished with a final-round 67.
'I had a pretty good shot at it,' Woods said. 'I had two bad swings, that cost me.'
Davis Love III, the 2000 champion, finished alone in third place at 16-under-par 272. A birdie at the 18th and Love would have matched Harrington's course-record 63 from Saturday, but Love landed near where Woods went and a bogey dropped him to a 65.
Ryder Cup partners Colin Montgomerie and Bernhard Langer shared fourth at 15-under-par 273. Jim Furyk, the first-round leader, shot a 4-under 68 and came in sixth at minus 14.
Chris DiMarco had the lowest round of the day on Sunday with an 8-under 64. He took seventh place at 275, one shot better than 2001 PGA champion David Toms and Nick Price.
Phil Mickelson, who will team with Toms in next week's WGC-EMC World Cup, carded his second consecutive 68 to come in 10th at 10-under-par 278. Retief Goosen, the 2001 U.S. Open winner, was a stroke behind Mickelson at 9-under.
Michael Campbell and Vijay Singh shot matching rounds of 69 to tie for 12th at minus 7. Mark O'Meara came in 14th at 5-under-par 283, followed by Bob Estes at 4-under par and reigning PGA champion Rich Beem, who was the only player over-par at 2-over 289.
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