The Northern Irishman rises to second spot alongside the Englishman who fell from the number one spot after a double bogey on the 18th. Fred Couples and Jason Dufner share the top.
Rory McIlroy puts himself back into contention as Lee Westwood falters
England's world number three, ahead by one after an opening 67, still held that advantage until he missed the 18th green, chipped 10 feet past and three-putted for a six.
A one over par 73 dropped the 2010 runner-up to four under for the opening major of the season and gave Fred Couples - champion 20 years ago and now 52 - the distinction of being the oldest halfway leader in the tournament's history.
After a best-of-the-day 67 Couples shares top spot with fellow American Jason Dufner on five under, one in front of Westwood, McIlroy, Sergio Garcia, Louis Oosthuizen and Bubba Watson.
McIlroy reached five under before failing to get up and down from a bunker at the 17th, but then saved par from off the final green for a fine 69.
This, of course, after he began the event with a double bogey six on his return to the course where he led by four with a round to go last April, then crashed to an 80.
Four-time winner Woods, though, is eight behind and survived the cut with only two shots to spare after an error-ridden 75 - and as he kicked his club away in disgust after hitting into sand on the short 16th three-time winner Sir Nick Faldo gave his verdict.
Commentating on American television Faldo said: "I think we can officially say that Tiger has lost his game - and his mind right now.
"He has not got a clue how to get the clubface onto the ball."
It was shocking to see - only two weeks ago Woods won at Bay Hill by five shots.
Westwood said of his own finish: "It was disappointing, but if you get out of position on this course it can punish you.
"These things happen and they will happen to everybody."
Henrik Stenson was leading when he took eight on the hole yesterday.
"I thought I made a few putts that didn't drop," added Westwood, "but I'm right in there for the weekend and that's where I want to be.
"The greens are getting more fiery and the wind is making it tricky."
He also had to contend with much cooler conditions earlier in the day.
McIlroy had finished his opening 71 with back-to-back birdies and said: "That was huge and it was nice just to get up today and get straight back at it.
"It put me in a positive frame of mind. I know I am playing well - my recent results (only one finish outside the top five since last August) show that.
"I just wanted to come and play and put myself in position to win another tournament, another major."
Two months after his Masters meltdown a year ago he won the US Open by eight.
Couples, captain of the American Presidents Cup team last November, described it as "a little bizarre" to find himself leading again after a "magical" round.
But it was not totally surprising. He has finished sixth and 15th the last two years and stated: "It's my favourite place in the world to play.
"On the range I felt my body tightening up a bit and I just wanted to play solid."
Phil Mickelson had been four over after a triple bogey seven at the 10th on the opening day, but he followed up his 74 with a 68 to be two under and despite the 18th playing so tough into the wind he birdied it from 18 feet.
Paul Lawrie birdied the last three holes for a 72 and on three under is still inside the top 10 in his first Masters since 2004.
Ian Poulter reached two under, but he went in the water for a double bogey at the short 16th and after a second successive 72 is alongside Justin Rose and Padraig Harrington.
Poulter said: "I'm a little bit disappointed - it obviously leaves a little sour taste."
He much preferred to remember his birdie on the 13th, where his second shot went into the bushes, but he was able to get at it and produced a magnificent chip to four feet.
"I had to take a little bow after that one. It was very cheeky, I must say."
Graeme McDowell (72) made it through on three over, as did world number one Luke Donald, Ross Fisher and Martin Laird on four over.
Open champion Darren Clarke, though, crashed to an 81 and 10 over playing with Couples, while Paul Casey's slow recovery from his shoulder dislocation - suffered snowboarding on Christmas Eve - saw him exit as well on seven over.
Ian Woosnam's second successive 77 meant he was alongside Clarke, with Simon Dyson (77) one further back and Sandy Lyle (86-78) was last.
Woods said: "I didn't quite have it with my swing today, but just tried to give everything on every single shot.
"I just need to cut the deficit tomorrow and then get off to a quick start Sunday."
Last year he was seven behind with a round to go and got into a tie for the lead before dropping to fourth.