Furyk, 42, who was born in West Chester and played his junior golf in the Lancaster area, checked in with an even-par 70, beating Woods by a whopping 5 strokes. He concluded three rounds at 1-under 209, tied with McDowell, who fired a 68.
Woods' 75 shocked a golf-crazed public who expected him to seize control of the championship and get a leg up on his 15th career major. But it was Furyk who exhibited the better play, carding three birdies and three bogeys after going 2-over through five holes.
Woods bogeyed two of his last three holes and fell back into a tie for 14th place at 214. He has never come from off the pace in the final round to win any of his previous majors, and his chances of winning his first since the 2008 Open appear extremely slim.
"It was just a tough day all day," Woods said.
Furyk went 4 of 5 on sand saves, missing out only at the par-5 16th hole where he made a bogey to fall behind McDowell, who birdied the 18th with a 4-foot putt. But Furyk came back with a 15-foot birdie putt at the shorter par-5 17th, and 2-putted the treacherous 18th green from 20 feet above the hole.
The winner of the 2003 Open at Olympia Fields near Chicago, Furyk got back to even par for the day by sinking birdie putts of 10 feet at No. 7 and 15 feet at No. 11. The birdie on the seventh came after he hit his tee ball on the drivable par-4 into a greenside bunker.
He also came out of bunkers to save par at the second, 12th, and 14th.
McDowell, who played the first two rounds of the Open with Furyk, said after the second round that the way to win the national championship at the Olympic Club is to "play Jim Furyk golf."
McDowell, the 2010 Open champion down the coast at Pebble Beach, didn't have Furyk competing beside him on Saturday but he took his own advice to heart with three birdies and just a single bogey.
As for what he likes about Furyk, the 32-year-old McDowell said, "He doesn't take chances he doesn't have to take on. He gets it back in the fairway. He putts well, holes out well. He takes his chances when it comes. And that's my type of golf as well."
Woods stumbled out of the gate with three bogeys on the first six holes, and 3-putted the eighth hole for yet another bogey. He appeared to right the ship with a 15-foot birdie putt at No. 9 but couldn't manage another birdie the rest of the day.
He 3-putted the long 16th for a bogey-6 and, instead of reaching the shorter par-5 17th in 2, he dumped his second shot in a front bunker and didn't get up and down.
"I'm still in the ballgame," said Woods, who is 5 shots off the pace. "It's not like you have to shoot 62 or 63. It's the U.S. Open."
A number of players came out of the pack to put some heat on the leaders and get into position for Sunday.
Fredrick Jacobsen ended the day in third at 211 after a 68. Two-time Open champion Ernie Els and Lee Westwood, the world's third-ranked player who is 0-for-56 in majors, were both at 212, with Els shooting a 68 and Westwood a 67.
David Toms, who with Furyk and Woods started the day 1-under, shot a 76 and tied for 18th at 215.
Contact Joe Juliano at 215-854-4494 or firstname.lastname@example.org or follow him on Twitter @joejulesinq. Read his blog, "Golf Inq," at philly.com/sports/golfinq