Low scores were plentiful due to soft greens, with heavy-hitters Rory McIlroy and Justin Thomas among a group tied for seventh on 65.
But British Open champion Francesco Molinari was not among those going low, battling to a 70 in his first round since Carnoustie.
"My whole game was great today," said Poulter. "As silly as it sounds, I would have liked to have nicked another couple but any time you shoot eight-under-par on this golf course it's a great round of golf."
Poulter said his record of never having a top-10 finish at Firestone was a source of motivation.
"It fires me up," said the Englishman. "It’s frustrating to look at. I wrote all of (the results) down (and) they were that bad.
"I was like 'seriously, how can you play a good golf course this many times and not really have a result?' To not even finish in the top 10 is pretty poor."
He also is focussed on qualifying for the European team for the Ryder Cup against the United States late next month.
"I want to play in it," he said.
Woods followed up a fine effort at the British Open, where he tied for sixth, with a decent first round score though the 14 times major champion was poised to hand in an unblemished card until a bogey at his final hole.
"I didn't really have it today with my ball striking but just hung in there, missed the ball in the right spots and made a couple of putts," said the 42-year-old.
"I just couldn’t quite get a feel for it (the driver). And even with my irons I wasn’t very sharp on the back nine.
"But I was just kind of hanging in there with it. Wasn’t exactly what I wanted to do today but I ground out a score."
(Reporting by Steve Keating in Toronto and Andrew Both in Cary, North Carolina; Editing by Ken Ferris/Peter Rutherford)
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