Laird, who landed his victory in the event a decade ago, carded four birdies as he signed for a three-under-par 69, matching the morning’s work of Dundee-based Frenchman Victor Perez.
The efforts left the pair sitting just three shots off the lead, shared by McIlroy as the 2018 champion saw his game click into gear and Canadian Corey Conners.
Laird birdied the 13th, 15th and 16th on his outward nine, which he finished by dropping his only shot of the day when he missed a three-footer at the 18th.
However, the Denver-based Scot repaired that damage with a birdie at par-4 third in a polished performance coming home.
“Very happy with that,” he declared afterwards. “It was a little breezy out there, especially early and cool this morning, so both front nine and back nine the first three, four holes are some tough holes.
“I was really pleased to get off to a good start through my first four, five holes and then just kind of kept it going.”
This week’s event is being played in front of some fans, with a 25 per cent capacity being allowed as tournaments on the PGA Tour start the process of trying to return to a normal environment.
“It's nice to hear some cheers and a little bit of energy from the fans,” admitted Laird. “It was fun to play in front of a crowd again.”
The Glaswegian landed his fourth PGA Tour title triumph in Las Vegas in October, securing his Masters return next month after an eight-year absence.
“I feel like I'm playing pretty well,” he said. “I've been hitting it nicely the last few weeks, my results just haven't been here.
“This is a course you got to stay patient on. It's a tough golf course. You have got to drive it good and then take your chances when you get them.”
McIlroy made his score with a burst of five straight birdies coming home to sit a shot ahead of US Open champion Bryson DeChambeau.
“I saw a lot of really positive signs out there today, which is really encouraging,” said McIlroy, who has finished tied sixth or better in four consecutive appearances in the event.
“I feel like you don't have to do anything special to shoot a good score here,” added the four-time major winner. “You can be really conservative off the tees, if you want to be.
“I think the toughest thing about this course is the par-3s and I played them in 3-under today. So that was a bonus.
“But I've watched Tiger enough here over the years and the way he played this course was, he played it very conservatively, he took care of the par-5s, and that was usually good enough to get the job done.”
Bob MacIntyre marked his debut in a regular PGA Tour event with a one-under-par 71 to sit in a tie for 29th.
The 24-year-old birdied two of those par-5s, the sixth and 16th, with his sole dropped shot coming at the ninth after missing the green on the right,
Russell Knox, the third Scot in the field, lies in a tie for 71st after a mixed bag in his opening 74.