Scotland's Laird became the first European to win the event at Bay Hill Resort in Florida with an 8-under 280, one stroke better than Steve Marino.
Marino held a late lead but bogeyed the 15th and double-bogeyed the 17th to fall off the pace, finishing at minus-7. He managed to birdie the 18th Sunday, ending with an even-par 72.
Sharing third place were David Toms (72), Justin Rose (68) and Marc Leishman at 6-under 282.
Six-time Bay Hill winner Tiger Woods was working on an unblemished round until closing with a bogey and double-bogey. He ended tied with 1997 winner Phil Mickelson and others for 24th place at 1-under 287.