Laird carded five birdies, including a key bird on No. 16 after coming off two straight bogies. He finished at 11-under-par 205, taking a lead into the final day of a tournament for the third time in his PGA Tour career.
First-round leader Spencer Levin retained sole hold on second place at minus-9 after logging a 1-under 71 Saturday.
Bubba Watson (68) and Steve Marino (71) shared third place four shots back at minus-7.
Six-time Bay Hill champion Tigers Woods, meanwhile, stumbled to a 2-over 74, matching his third-worst score on the course as a professional. He ended sharing 29th place at minus-1.