World number one Rory McIlroy had to settle for an even-par 72 after finding water at the par-three 17th, famous for its island green, while Tiger Woods risks missing consecutive cuts for the first time as a pro after shooting a two-over 74.
American Blake Adams' six-under-par 66 set the early pace at sun-blessed TPC Sawgrass while compatriots Kevin Na and Ben Crane were lurking a further shot back at an event that is widely regarded as golf's unofficial fifth Major.
Laird was the only player to finish the challenging course bogey-free and once again his accomplished putting was the key.
"Any time you go around this golf course bogey-free is obviously a very good day," said Laird, who won in Florida last year, clinching the Arnold Palmer Invitational at Bay Hill.
"I missed a few greens out there from good spots in the middle of the fairways but managed to scramble really well and chipped them up close enough ... but the key was the putter and any time I had a chance for birdie, I rolled it in."
Poulter, who finished second here in 2009, made just one bogey and had a run of nine single putt holes in what was a confident round.
"It was a very, very good round of golf. That's definitely in the top 10 of the rounds of golf I've ever played," he said.
Woods, who missed the cut last week at Quail Hollow, runs the risk of another embarrassing early exit after a frustrating round that left him in a tie for 100th place.
With a large crowd following Woods and playing partner Rickie Fowler in glorious sunshine, the 14-times Major winner did prompt some cheers with a birdie at 17.
But that was a rare bright spot for the former world number one who is still struggling with his game and made five bogeys.
"I hit three decent shots in there and got some of the worst lies. The best shot I hit all day was on 3 and I ended up in a spot where I really couldn't play from," said Woods.
"It was frustrating in the sense that my good shots ended up in bad spots and obviously my bad shots ended up in worse spots."
Fowler, fresh off his first US PGA Tour win at last week's Wells Fargo Championship, mixed four birdies with four bogeys for an even-par 72.
World number two Luke Donald recovered to make even-par with birdies on the 16th and 17th, while defending champion K.J. Choi shot a three-over 75.
The worst performance at the popular 17th hole came from Argentine Angel Cabrera, who found water three times as he made a nine. Cabrera later withdrew, citing personal reasons, one of five players to pull out of the tournament on the opening day.
Lee Westwood, ranked third in the world, finished the day one-under along with Phil Mickelson, the 2007 Players winner.