The Glasgow exile, who had shared top spot after a sparkling opening card of 65, spilled four shots on his final three holes in a one-over 73 which dropped him to a six-under aggregate of 138.
Laird, a two-time winner on the PGA Tour, had been making good progress at three-under for the day through 15 but his day began to unravel when he plunged his second shot to the long 16th into the water and racked up a bogey.
The former Scottish Youth's champion then found the same lake with his tee-shot at the island green 17th which cost him a double-bogey 5 before he left a chip short on the last and bogeyed again. From leading the field by two strokes at one stage, Laird suddenly found himself off the pace set by former Masters winner, Zach Johnson, who shot 66 for 136.
"That's what this course will do to you," lamented Laird. "I got a bit greedy with a four-iron to the 16th – it was a stupid shot – and was between clubs at the 17th.
"A nine-iron was too much and a wedge not enough, but I didn't hit it solid and the wind got it. It was a bad shot.
"But as big a car crash as I just had, I'm still well in it. I'd have taken my position before the start."
Despite his late collapse, Laird remained in the hunt but world No.1 Rory McIlroy was disappointed to have missed the cut at Sawgrass for a third successive time, with a 76 for 148.
Meanwhile, at the Madeira Islands Open, Alastair Forsyth was heading into the weekend in a share of 16th place.
The Paisley man, who won the title in 2008, added a 68 to his opening 69 for a seven-under 137 to finish five strokes behind former Ryder Cup player Oliver Wilson, who charged to the front with a 65 for 131.