Laird eagled the 15th hole and saved par at the 16th after hitting into the water, finishing the day at 19-under 194, one stroke better than second-round leader Jonathan Byrd.
Laird has done well at TPC Summerlin in Las Vegas. The 27-year-old Scotsman's only other PGA Tour win came at the course last year following a three-way playoff with Chad Campbell and George McNeill.
Byrd made a charge at the end Saturday, closing with a birdie to pull within a shot of the leader. He placed his approach to within a couple feet of the pin at the 18th and closed out the round with a 66, improving to minus-18.
Cameron Percy (62) and Webb Simpson (64) shared third place at 17 under 196.