Garcia and Thompson each finished at 5-under-par 65 on the par-70, 7,140-yard PGA National course. The round was halted at 6:35 p.m. ET because of darkness with three players still on the course. That trio will finish Friday morning before the second round gets underway.
The highlight of Garcia's round was holing out an 8-iron for eagle on his second hole. He ended with a birdie on his final hole.
Garcia's eventful round included a bogey on the par-4 sixth hole after his tee shot found the water and he hit out of the hazard with an alligator looking on.
"That was probably one of my worst drives," said Garcia, who is seeking his first win on the PGA Tour since the 2012 Wyndham Championship. "I pulled it a little bit there. I was more worried about the alligator that was on the other side of the island than getting out of the water, because the ball, I could see probably half of it.
"So I knew that I could get it out, didn't know how far out, but then I managed to hit a pitching wedge and came out a little bit low, but it got a little bit of run. Almost made 4, which would have been a great 4. I'm not going to lie, I was happy with a 5."
Thompson, the tournament winner in 2013, also closed out his day with a birdie for a share of the lead.
One shot behind the leaders were Rickie Fowler, who is No. 5 in the World Golf Rankings, and William McGirt at 4-under 66. Fowler was the only finisher without a bogey, and McGirt, seeking his first career tour victory, closed with three consecutive birdies.
Phil Mickelson opened with a 1-under 69. Rory McIlroy, No. 3 in the world, finished with a three-putt bogey from 10 feet on No. 18 for a 2-over 72. McIlroy is the highest-ranked player in the field this week.