Williamson, playing on a sponsor's exemption, bested his second-round co-leader David Toms, and first-round leader Mahan over the final four holes to finish 11-under par after 54 holes.
'I wasn't really looking at the leaderboards,' he said. 'I figured if I could just keep making birdies, making good swings, I've got 18 holes and we'll figure it out tomorrow.'
He hit an 8-foot birdie putt on the par-4 No. 15 to go 11-under and made par the rest of the way, nearly chipping in for birdie on the 18th.
'I don't usually get excited on the golf course,' he said. 'But if that ball would have gone in, I don't know what I would have done.'
Toms, a 12-time winner on TOUR, including the 2001 PGA Championship, has five top-10 finishes this year. But he bogeyed the par-3 16th, and he fell two back after his drive on the signature 17th hole found the water.
His 69 was good enough for third place a stroke behind Mahan, who shot a 67.
'I'm in good shape for tomorrow,' Toms said. 'I just have to keep playing. I feel I can play this golf course well.'
So can Mahan, who finished second here a year ago. He had a tournament-best 62 Thursday and hit 71 on a windy Friday. He said there is just something about the course that brings out the best in his game.
'You just see the greens a little better than in most places,' he said. 'You see your tee shots better, the yardage seems better, just everything is easier for you.'
Williamson, 40, is a regular on the Nationwide Tour who graduated from nearby Trinity College in Hartford, where he played baseball and hockey.
He says he didn't even know this Tour event existed when he was in school.
Now he's playing for a two-year Tour exemption.
Williamson was trailing by one when he birdied No. 15. After Toms and Mahan bogeyed the 16th, he saved par to take sole possession of the lead.
Fred Funk, a gallery favorite, shot a 67 to finish alone in fourth place.
Pat Perez and Nick O'Hern were four back at 7-under. O'Hern, who shot a 66 Saturday, has never won on tour, but finished second at last season's Booz Allen Classic, which also came just after the U.S. Open.
'The thing about this week is that everything is going to seem a bit easier,' O'Hern said.
Vijay Singh also shot himself back into contention with a 66. He hit birdies on Nos. 2 and 3, bogeys on Nos. 4 and 5, and then hit his second shot on the par-5 6th hole to within 5 feet of the pin and made an eagle.
'I told my caddie we need to shoot at least six-under to be back in it,' he said. 'It's not impossible to catch but it's up to me what I'm going to do tomorrow.'
Stewart Cink was within three shots of the lead when he imploded on the par-4 15th hole. He lost his drive in the woods, had to take a drop after hitting his second drive in almost the same spot, had another penalty stroke, and eventually shot a 10.
Mahan also went right on the 15th, but his shot hit the cart path and bounced left missing a spectator by inches before landing in a green-side bunker. From there, he managed to save par.
'It's a feast-or-famine hole,' Mahan said. 'It's a great, great hole -- risk, reward.'