Laird three-putted on four occasions over his inward nine sliding from one under par after seven holes to finish with a two-over 74.
It left the North Carolina-based Scot trailing the leader Justin Rose by nine shots. The Englishman posted a blistering seven-under par 65 to upstage playing partner Tiger Woods by four shots.
The American is seeking an eighth win in this event, one that would take him back to No. 1 in the world for the first time since October 2010.
Rose, who lives 30 minutes from the Bay Hill course and is a previous winner here, looks in the form to deny him. Despite bogeying his second hole but then snatched an eagle and six birdies, including four in succession from his 13th a haul that required just 21 putts.
"I'm a little surprised by that number but anytime you go low at Bay Hill it's a bonus but starting out this morning the first five, six to eight holes felt a grind as it was cold and it was windy," said Rose. "You had to go out and play well and you couldn't fake it out there.
"But not all parts of my game were perfect but I have to say the putter was really, really hot and they're fun days when that happens, and it was one of the hottest days I've had for some time with the putter."
Laird dropped a stroke at his first hole, the 10th when his second shot flew the green and he took three more to get down. The Scot pulled off a brilliant 170-yard second shot at his sixth that landed just two feet from the flag for birdie and made it back-to-back circles on his scorecard at the next when he two-putted from 50 feet.
His inward half was marred by three-putt bogeys at his 10th, 16th and 17th holes.