Woods drained a 12-footer on the 18th to force a play-off
Tiger Woods birdied the last to force an 18-hole US Open play-off against fellow American Rocco Mediate at Torrey Pines on Monday.
Woods, who led by one shot overnight, continued to struggle with a painful left knee but drained a 12-footer on the 72nd hole to keep his hopes alive.
The 32-year-old is bidding to claim a 14th major title, while the 45-year-old Mediate is chasing a maiden major.
Lee Westwood missed his putt on 18 to make a play-off and finished third.
Mediate, two back overnight, carded a level-par 71 for one under in the penultimate group and then sweated as Woods and Westwood played up the par-five 18th.
Both players found bunkers off the tee and made the green in three but Westwood left his 20ft birdie putt short for a 73 to end level par overall.
Woods had already shown, if anyone needed reminding, that he was capable of the sublime after firing 30 on the back nine on Friday and surging to the top of the leaderboard on Saturday with two eagles and a birdie in his last six holes.
And the world number one drew another exultant roar from the crowd when his putt dropped on the final green for a 73 to book a 1700 BST head-to-head with Mediate.
Unbelievable. I knew he'd make it
"Unbelievable. I knew he'd make it," said Mediate, the world number 158, who scraped through qualifying via a play-off and won the last of his four PGA Tour titles in 2002.
"I will just have to get ready for a battle royale tomorrow.
"How many opportunities does anyone have to go up against the best player on the planet in the US Open?"
Woods, who won the US Open in 2000 and 2002, said: "I was thinking, 'just stay committed to the stroke'.
"It took forever to break but in the last little bit it fell in."
Woods, who has won all 13 of his major titles when leading going into the final round, began the last day with his third double bogey of the week on the first hole at the par-71, 7,643-yard South course.
He followed that up with a bogey and was clearly in pain from the left knee that was operated on for a third time two months ago.
Westwood, one adrift of his playing partner overnight, also bogeyed the 1st, handing Mediate the lead, and from then on it was effectively a three-way battle.
Woods, who has won six Buick Invitationals at Torrey Pines, shrugged off the discomfort to grind out a series of pars, while Mediate fell back and Westwood took a one-shot lead at two under after nine holes.
But Westwood dropped three shots in four holes after the turn and Mediate regained the lead when Westwood and Woods made a joint hash of the 13th.
Woods rejoined Mediate when his countryman bogeyed the 15th but slipped back again following his own mistake soon after.
Westwood, meanwhile, held his nerve to fight back to level par alongside Woods before falling short in the grandstand finish on 18.
"I'm a little bit gutted but pretty satisfied generally," said Westwood, who was aiming to be the first European winner of the US Open since England's Tony Jacklin in 1970.
"I think I've proved to myself and a few others that I think there is a major championship in me."
It will be the first play-off at the US Open - the only major that stages a full 18 holes of overtime - since Retief Goosen defeated Mark Brooks at Southern Hills in 2001.
"We will have fun. Rock is a great guy," said Woods, who has won 14 of his 15 play-offs in worldwide tournaments, including two majors.
Behind the top three, Sweden's Robert Karlsson climbed up the leaderboard with a level-par 71 to end two over alongside American DJ Trahan.
US-based Swede Carl Pettersson, American John Merrick and Spain's Miguel Angel Jimenez finished three over.
American Heath Slocum fired a six-under 65, the round of the week, to climb to four over for the tournament.
South Africa's two-time champion Ernie Els was edging into contention until a triple-bogey seven at the 15th ruined his chances, while Australia's 2006 champion Geoff Ogilvy fell back after a 74 for four over.
Local favourite Phil Mickelson, still chasing a first US Open win, made three birdies in the last five holes for a 68 but was undone by Saturday's 76 to end six over.
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