Former British Open champion Lehman shot a five-under-par 67 while overnight leader Baird carded a 68 as both players finished on 17-under 199, one stroke ahead of Scott Verplank (65).
Cameron Beckman was in fourth place on 201, with Singh, Tim Clark of South Africa, Mark Calcavecchia and Australia's Geoff Ogilvy all on 202, 14 under.
After cramming eight birdies in his seven-under 65, Singh said he fancied his chances of pulling off a fourth successive victory.
"I got myself back in there," he told reporters. "I've got a good chance tomorrow. I need to make a few birdies to catch up early."
Singh has won eight times on the PGA Tour this season, including five of his last six starts.
The 41-year-old Fijian birdied five of his first seven holes on Saturday before adding three more in the opening four holes of the back nine at the Magnolia course.
Singh is one of 20 players within five strokes of joint leaders Lehman and Baird.
For the third consecutive week, Lehman, 45, who has not won for four years, finds himself leading the field after 54 holes.
He tied for second at the Las Vegas Invitational before finishing joint fourth at the Greensboro Classic last week.
Lehman missed a five-foot birdie putt at the 18th on Saturday that would have given him the outright lead.
"I feel like I had a great game plan over the last two weeks," he said. "I feel like I was very calm on the golf course and very focused and played well and just made a couple too many mistakes.
"Sometimes mistakes just happen, so you can't always control everything. But the good news is I made plenty of birdies the last couple of weeks, so I'm making plenty of putts and doing plenty of good things well."
His plan for Sunday is simple, make a lot of birdies.
"Tomorrow I'm going to need to go low here," Lehman said. "I'll have to go out and shoot 64, no doubt about it."
South African Clark produced the best round of the day, an eight-under 64, to surge from joint 34th to a tie for fifth.
Former British Open champion Ben Curtis headed a group of four players on 203. Also on that mark were Joey Sindelar, Australia's Mark Hensby and Stephen Ames of Canada.