Charles Howell III, who was tied for the overnight lead with Kenny Perry, fired a 67 for an eight-under total of 134 to move one stroke clear of Fred Funk (67) at the top of the leaderboard.
South Africa's Retief Goosen (67), the winner of last week's Chrysler Championship, was third on 136. Chris Riley was fourth, a further shot back, with David Toms, Chris DiMarco and Justin Leonard joint fifth on 138.
Woods and Singh, the world number one and number two respectively, are battling for the PGA Tour Player of the Year and the U.S. money-list crowns.
The American, who has won five PGA Tour titles this year, is two-under for the championship on 140, one ahead of Singh who leads Woods in the money-list race by $768,494.
If Singh, who has four victories to his credit in 2003, finishes joint third or better, he will be the tour's top money winner. Woods has been top of the order of merit every year since 1999.
GOOD FRIEND
Woods, playing with his good friend Ernie Els, struggled in his second round with only two birdies and a lone bogey but still stayed in touch with the leaders.
"A lot of guys have a chance to win," Woods told reporters. "I'm right up there with those guys.
"Obviously, tomorrow's going to be a very important day to see if I can put myself in position come Sunday."
After opening with a mediocre two-over-par 73, Singh turned his game around on Friday with four birdies and one bogey.
"That was the easiest 68 I could have shot," Singh said. "I left a lot of shots out there but it's very hard to read the greens."
After taking 34 putts on day one, the tall Fijian needed only 26 in round two.
"I played on Bermuda for the last three, four weeks and I just have never played these Bermuda greens before. They are just so difficult to read," Singh said.
Woods and Singh are both trying to catch the 24-year-old Howell, who has only one win in his short career.
Howell made his move on the par-five ninth when he recorded his first birdie of the day. He then went bogey-eagle-birdie from the 12th to the 14th.
"It's funny how the whole round was right in those three holes there," Howell said. "That was really, really, really important there."
