AKRON, August 1, 2013 (AFP) - Despite a bogey on his final hole, the par-four ninth, Simpson finished the first round of the World Golf Championships event with a one-stroke lead over Sweden's Henrik Stenson.
World number one Tiger Woods was among a group of four players sharing third place, two strokes off the lead.
Woods, a seven-time winner at Firestone Country Club, was joined at four-under by England's Chris Wood, Ryan Moore and defending champion Keegan Bradley -- who had four birdies and no bogeys.
Woods's effort included six birdies and two bogeys. He hit 10 of 14 fairways and all but two greens in regulation.
"It was a little blustery today," Woods said. "Wind was up, greens were soft. But at least the ball was flying. It was warm, ball was going, and even though it was a little more wet because of the rain, with it being this warm, the ball is still traveling. We got it out there pretty good."
Phil Mickelson, teeing it up for the first time since winning the British Open, carded a two-over par 72.
"I certainly didn't want to shoot over par and leave myself this far back after the first day," Mickelson said. "But my game feels sharp. I feel like I'm rolling the ball well. I know I'm swinging the ball well, and tomorrow if I can just mentally see it a little clearer, I should have a good day."
Northern Ireland's Rory McIlroy, who will defend his PGA Championship title next week, recovered from a double bogey six at the par-four 10th to finish at even par 70 for the round.
Leading first-round scores on Thursday in the World Golf Championships Bridgestone Invitational (USA unless noted, par-70)
64 - Webb Simpson
65 - Henrik Stenson (SWE)
66 - Ryan Moore, Chris Wood (ENG), Tiger Woods, Keegan Bradley
67 - Jason Dufner, Bubba Watson, Rickie Fowler, Bill Haas, Jim Furyk, Luke Donald (ENG)
68 - Scott Piercy
69 - Kiradech Aphibarnrat (THA), Ian Poulter (ENG), Paul Lawrie (SCO), Zach Johnson, Justin Rose (ENG)
70 - Harris English, Gonzalo Fernandez-Castano (ESP), Jonas Blixt (SWE), Ken Duke, Peter Hanson (SWE), Richard Sterne (RSA), Satoshi Kodaira (JPN), Francesco Molinari (ITA), Jamie Donaldson (WAL), Rory McIlroy (NIR), Paul Casey (ENG), Branden Grace (RSA)
71 - Matteo Manassero (ITA),Nick Watney, Bo Van Pelt, Graeme McDowell (NIR), Lee Westwood (ENG), Miguel Angel Jimenez (ESP), Steve Stricker, Sergio Garcia (ESP), Ernie Els (RSA), David Lynn (ENG)