Woods fired a 7-under 65 on Sunday to take second place at 9-under-par 279. He nearly overcame a nine-stroke deficit at the start of the final round but took his second runner-up finish in as many years.
'I got into a rhythm on the back nine and I just got it going,' said Woods. 'It's fun when things like that happen. You pick a target and hit it and all of a sudden, it just turns out.'
Padraig Harrington, last year's winner, shot a 1-under 71 on Sunday and finished in third place at minus-6. Justin Leonard (71) and Masters champion Mike Weir (72) shared fourth place at 4-under-par 284.
Woods had the opportunity to win and to erase the biggest final-round deficit in his career. But Love was steady down the stretch when it mattered.
Love held a three-shot lead as he made his way to the par-3 12th. He missed the green with his tee ball, then ran his pitch 50 feet past the hole. Love's par-saving putt flew six feet past the cup and he missed that to record a double-bogey.
Woods was in the clubhouse at 9 under par and only one behind Love. Love missed long birdie putts at 14 and 15 but drained a 55-footer for birdie at the par-3 17th after his approach spun back down a ridge.
With a two-shot lead, Love knocked his approach in a greenside bunker at the 18th. He blasted to a few feet and tapped in for the victory, his second at this event.
'When he birdied five holes in a row, I knew the game was on,' said Love, who also won in 2000. 'And I had to play hard.'
Woods was 2 under on his round after 10 holes and then he really started to play well. At the 11th, Woods chipped in for birdie from the side of the green. At No. 12, Woods holed a 15-footer, then one hole later it was a routine two-putt at the par-5.
Woods drained a six-footer for birdie at the 14th and made it five in a row with a seven-footer at No. 15.
'When I birdied the 15th, I thought if I could birdie the last three holes I would have a chance to win the tournament,' said Woods, who won this title in 2001.
Trouble loomed for the No. 1 player in the game. He pushed his second shot right into a hazard and after a drop, Woods hit his fourth to 18 feet. He rolled home the par putt to stay in the hunt.
Woods had a pair of 30-footers for birdie at the last two holes but neither fell, so it was a question as to whether or not Love could hold on and win, something he did four times on the PGA Tour this season.
Love took the lead after a course-record-tying 63 in Saturday's third round. He collected birdies at two and five but some suspect putting stalled his good start. Love missed a 15-footer for par at the seventh then missed on a five-foot par putt two holes later.
Love birdied the 11th but dropped two strokes at the next hole thanks to an errant tee shot and a poor chip. He played well enough to get the win and the $1,200,000 first-place check, the biggest of his career.
'We both made a lot of mistakes this week,' said Love, referring to himself and Woods. 'I got a couple of good breaks. I was fortunate to hang in there.'
K.J. Choi, who was in second place at the start of the round, struggled to a 5-over 77 and took sixth. He finished at 3-under-par 285, one shot better than the tour's leading money winner Vijay Singh, who carded a 2 under 70 on Sunday.
Robert Allenby finished at 1-over-par 289 and took eighth. Fred Couples was a stroke behind Allenby after a 4-over 76 in Sunday's final round.