Corey Conners leads the way at the halfway stage at the Orlando venue on nine-under, but the Canadian has Scot Laird, Norwegian Viktor Hovland and Northern Irishman Rory McIlroy all breathing down his neck in the $9.3 million event.
Also in the hunt in a tournament won by McIlroy, Francesco Molinari and Tyrrell Hatton over the last three years are English quintet Paul Casey, Justin Rose, Lee Westwood, Matthew Fitzpatrick and Tommy Fleetwood.
Laird, who landed the second of his four PGA Tour title triumphs in this event a decade ago, added a 67 to an opening 69 to sit on eight-under, one behind Conners.
The 38-year-old Scot, who had come into this week on the back of three straight missed cuts, lit up his day with a brilliant eagle-3 from 12 feet at the 12th while four birdies included a brace of 2s.
“I obviously have good feelings about this place after winning here,” admitted Laird afterwards. “I’ve always liked this golf course.
“There are a lot of tee shots, especially coming down the stretch, that are left to right, and it has always suited my eye.
“The greens generally are pretty firm here and I hit it pretty high so that helps. It’s a fun place to come and have always liked it.”
The Denver-based Glaswegian, who has former Scottish Amateur champion Kevin McAlpine on his bag at the moment, returned to winning ways when landing a second Shriners Hospitals for Children Open in Las Vegas in October.
He then finished in the top 20 in the Sentry Tournament of Champions in Hawaii in January before suffering early exits in the Farmers Insurance Open, Waste Management Phoenix Open and, mostly recently, Genesis Invitational.
“I battled my game for a couple of weeks but then the last couple of tournaments my game was fine,” added Laird. “My mental game was a little off, I was getting a little impatient on the golf course.
“I made a conscious effort the second round in LA a few weeks ago and played a nice round there, narrowly missed the cut after a terrible first round and took that momentum into this week.
“I’m just trying to worry about myself. I didn’t even see a leaderboard until I saw it on the screen. I didn’t know where I was.
“I am just trying to take care of what I can do and see where that puts me at the end of the week.”
Conners, who shared the overnight lead with McIlroy, backed up his opening 66 with a 69 as he bids to add to a sole success in the 2019 Valero Texas Open.
McIlroy (71) and Hovland (68) sit on seven-under along with American Lanto Griffin (68), with US Open champion Bryson DeChambeau (71) on six-under.
Casey (69) and Rose (68) are in a group one further back along with debutant Jordan Spieth (69), with Fitzpatrick and Fleetwood both on four-under.
On his PGA Tour debut, Bob MacIntyre (71) sits joint-21st on two-under, with Russell Knox (71) also making the cut on one-over.