Woods closed the gap to one after a three-foot birdie putt on the par-5 16th and a scrambling par by Singh at the same hole. Woods had the honor on 17 and hit his tee shot into the right rough, causing him to pace around the tee box after slamming his club into the ground.
Singh played his drive left of the hole on the fringe but only 15 feet from the stick. He drained his birdie putt to reach 11-under-par while Woods ran into trouble from the side of the green.
Woods' second shot was impacted by mud on his ball and three strokes later, Woods was in with a double-bogey-5 and down by four.
'It was windy and blustery out there. I didnt figure it out all day,' said Woods, who finished with a 2-over 74 in the third round. 'I was long, I was short, I was left, I was right. It was tough out there. You could wait 15 seconds and your club selection would change three times.'
Singh was one of just three players who broke par on another windy Saturday with a 1-under 71 for a three-day total of 11-under-par 205. Woods is alone in second at 7-under while Bernhard Langer is third at minus 5.
'You had to be very careful out there. It was hard to judge distances,' said Singh, the 2000 Masters champion. 'This is a tough golf course when the wind blows. These greens are not easy to putt on with the undulations.'
Singh struggled to a 1-over 37 on the front side and dueled with Fred Couples for the lead throughout the opening nine. Couples fell off the lead with back-to-back bogeys at seven and eight but Woods was lurking near the top.
The three-shot swing at 17 was not the only one of the round between Singh and Woods. At the par-4 10th, Woods seemed to have a clear advantage as he bombed his tee shot into a greenside bunker, nearly hitting Couples, who was playing his sand shot in the group ahead.
Singh found the fairway with his drive but he had 52 yards, an awkward distance to play a full shot. He hit a lob wedge that hopped a few times before falling into the cup for an eagle 2.
Woods blasted out to four feet for what looked like an easy birdie, but he missed the putt and still had three feet coming back. That par save lipped out of the cup on the right side giving the tournament host a bogey and a four-shot deficit.
Both players birdied No. 11 but Woods inched closer to the lead with a six-foot birdie putt at the par-5 13th. Singh found the trees off the 14th tee and was forced to pitch out into the fairway. He failed to get up and down and took a bogey, dropping the lead to two strokes.
Singh and Woods both sailed the green at the difficult par-3 15th and left with bogeys but Woods got within one with a three-foot birdie at 16 after Singh was lucky to leave with par.
It was at 17 where the second two-shot swing of the round gave Singh a good chance at the $1 million first-prize check.
This season was a winless one for Singh and although he finished fourth on the PGA Tour money list and won twice on the European Tour, he would still like to visit the winner's circle.
'Everybody wants to win,' Singh said. 'I don't think anybody is trying to have fun.'
Langer may be in third place but he took an interesting path getting there. His second shot at the par-5 16th turned left and landed somewhere near a tree. Langer could not find his ball so he helped his caddie climb the tree before joining the search himself in the large oak. The ball was recovered and he saved par but posted a 74 for the day.
Couples once again found the 15th hole to be his nemesis like Friday, when he carded a double-bogey-5 after dropping it in the drink. On Saturday, Couples took the water out of play by blasting his tee shot over the green in an awkward lie. He hit too much ball on his second and the ball skidded across the green into the water. Couples hit from the same spot for his fourth but ran it past the hole and two-putted coming back for a triple bogey.
Couples, who shot a 77 in the third round, is tied for seventh with David Toms and David Duval at 2-under par.
One player who had a good round was Denmark's Thomas Bjorn. He fired an 8-under 64 to match the Sherwood Country Club course record originally set by Davis Love III, Woods and Sergio Garcia last year. Bjorn might be too far off the lead after Friday's 80 as he tied with Ryder Cup teammate Colin Montgomerie at 1-over-par.
Full-field scores from the Williams World Challenge