Woods shot a two-under-par 69 to slip a shot further back from Singh, who if he wins on Monday will take over from the American as world number one and move past the $7 million mark for earnings this year, eclipsing his 2003 total of $7,573,907 -- his best year on the PGA Tour.
A victory would also virtually sew up the Player of the Year award for the U.S. PGA champion who has five Tour victories this season.
Bill Haas shot an even-par 71 to stay in the hunt at nine-under-par and third overall while Japan's Shigeki Maruyama also shot an even-par 71 and is six shots behind Singh in fourth.
Jay Williamson and defending champion Adam Scott are tied for fifth at seven-under-par, while first round co-leader Ryan Palmer dropped to ninth place at five-under-par after shooting 74.
At 41, Singh is on the best run any golfer has had over the last two years with 30 top-10 finishes in the last 49 events and nine victories in two seasons.
Woods had five wins in three consecutive seasons from 2001, but since his triumph at last year's WGC American Express Championships in Atlanta, he has only one match play tournament victory to his name.
"It
"The wind conditions were different. I missed a few fairways through not thinking the right way and I have not played this course in this wind."
VERY PATIENT
Singh sank three birdies to make the turn at three-under-par 33, but had to wait until the final hole for his next birdie to cancel out a dropped shot on the 14th.
"You have got to be very patient," Singh said. That's the key. Normally when you have a lead and don't have a good start, a lot of guys press and try to get the shots back.
"You just go out there and play hole-by-hole, take your time and get settled in. That's what I do. I don't rush myself."
Singh's strategy was epitomised at the PGA Championship where he failed to beat par on any of the final 18 holes, but made a birdie on the first playoff hole to take a lead which he would not relinquish for his third major title.
The Fijian is also looking forward to being paired with Woods.
"I've played with Tiger many a times and I enjoy playing with him," he said.
"He's a great player.
"I'm ready to play tomorrow and am just going to go out there and try to win the golf tournament.
"Fortunately, Tiger is in my group and I can see everything happening."
Woods agreed.
"Vijay's been playing extremely well over the last couple of years and I think it would just be a blast to go out there and compete at that level," he said.