The 2011 PGA Championship winner doesn't want to stress out on defending his title.
"No, it's business as usual," he said. "I just want to not put too much pressure on myself to do anything crazy. I know this golf course fits me, so to let the course come to me is big here."
Another shot back at 67 in the star-studded field that includes 49 of the top 50 players in the world rankings were Furyk, Jason Dufner, Bubba Watson, Rickie Fowler, Bill Haas and Luke Donald.
Fowler spoke for a lot of players when he said that there are a lot of similarities between Firestone and Oak Hill, the site of the PGA Championship next week.
"If the course stays dry and it starts to firm up through the weekend, it's very comparable as far as you've got to drive the ball well and position yourself off the tee," said Fowler, who practiced at Oak Hill on Monday. "It's a great warm-up here, but obviously this is one of our bigger weeks of the year, too. Two great weeks, back-to-back, and two great golf courses."
While the world's top-ranked player, Woods, was in prime position, that wasn't necessarily the case for Nos. 2 and 3.
Phil Mickelson, coming off his dramatic victory at the British Open two weeks ago, struggled with his concentration and came in with a 72.
"Tonight I'll get a little bit more rest and try not to do too much and see if I can come out tomorrow a little bit more focused," he said.
He missed two par putts inside 3 feet on consecutive holes early in his round.
Rory McIlroy shot a 70. The defending PGA champion is winless this year.
Frequently accused of being too hard on himself, McIlroy looked at the positives.
"I'm just trying to enjoy myself this week, enjoy my golf, play with a bit more of a smile on my face," he said.
Then he added, "You have to have a positive attitude out there to play well. But saying that, it's easier to smile when you play well."