The world number one, engaging with the fans at every opportunity, rolled in a 20-foot putt at the 13th before sinking a 12-footer at the 15th on the way to a two-under-par 70.
“I want to be in contention and I’ve put myself right there,” Woods told reporters after parring the last three holes.
“On this golf course you can make up shots and you can lose shots. That’s one of the beauties of it. It should be an exciting weekend.”
In pursuit of a 15th major title in his first tournament for nearly five months, Woods posted a six-under total of 138 to finish level with playing partner KJ Choi of South Korea (71) and long-hitting American Ricky Barnes (70).
Britain’s Ian Poulter fired a five-birdie 68, his only blemish coming at the last where he missed a seven-foot par putt, to hold the clubhouse lead at eight under.
Fellow Englishman Lee Westwood was at nine under with seven holes to play, having raced to the turn in a sizzling four-under 32.
Only 18 players in the field were under par for the round with tricky pin positions and Augusta’s notorious swirling winds making club selection difficult.
Overnight leader Fred Couples followed his opening 66 with a three-over 75 after waking up with a bad back.
“For a while I felt like I could go from first to last,” the 50-year-old said after finishing bogey, bogey, bogey. “But I kind of loosened up and I got it around.”
Again watched by huge galleries on his highly anticipated return to competition after a self-imposed break of almost five months, Woods recorded his first birdie at the par-five second where he chipped in from just off the green to three feet.
ACKNOWLEDGED CHEERS
Wearing a green shirt, black sweater and black trousers, the American tipped his cap to acknowledge the cheers from the crowd packed around the second green.
Woods, who wore sunglasses in between every shot due to the glare and high pollen count, stumbled at the par-three fourth where he pulled his iron shot well left after twice changing clubs on the tee.
From behind the left greenside bunker, he hit a lob wedge to 10 feet but missed the par putt to slip back to four under overall.
Woods was again in crowd-pleasing mode, having promised on Monday to give more respect to the game and the fans following startling revelations about his extra-marital affairs at the end of last year.
After teeing off at the par-three sixth, he spotted a young boy wearing a baseball cap with ‘TW’ emblazoned on the front and he put a huge grin on the youngster’s face by giving him a friendly hand slap as he walked by.
Woods failed to birdie the par-five eighth which he had eagled the previous day, his wedge approach screwing back 75 feet from the pin and he did well to two-putt from there for par.
Out in level-par 36, he surged up the leaderboard with his birdies at 13 and 15, the first of them prompting him to raise his putter skywards in celebration.
Woods is bidding to become the first player to launch his season with a major victory since fellow American Ben Hogan clinched the 1953 Masters.