Starting from the 10th, Simpson had gone to the turn in 31 with birdies at the 13th, 15th, 17th and 18th and made it four birdies in succession when he picked up shots at the first and second.

A bogey at the third halted his charge briefly before further birdies at the sixth and seventh, but a superb round ended on a disappointing note with a bogey on the ninth.

Stenson had no such concerns after a flawless 65 that began with a birdie at the first and eagle at the par-five second, with the Swede picking up further shots at the 11th and 12th.

The 37-year-old, who finished three shots behind Phil Mickelson at Muirfield last month, has not played in the limited-field event since 2010, when he finished dead last in 80th place.

“In 2010 I played here with pneumonia I didn’t know about. Saved Tiger from finishing last though, which I’m sure he appreciated,” Stenson joked.

Woods finished joint 78th on that occasion but has also won seven times at Firestone and carded an opening 66 which featured a flawless inward nine of 31.

That was a feat matched by Bristol’s Wood, who prepared for the event at his home course of Long Ashton and expressed his thanks to greenkeeping staff by leaving some “cider vouchers” behind the bar.

“I have to mention James and the greenkeepers at my home club of Long Ashton for their help last week,” Wood wrote on his blog on his management company ISM’s website on Wednesday.

“He worked on getting the putting green nice and quick for me in preparation for my tournament this week. It was a pleasure to putt on it. I just hope the members did not complain too much. As a means of compensation, I made sure cider vouchers were left behind the bar for everyone to enjoy a drink.”

Compatriots Ian Poulter and Lee Westwood, both third in the Open in differing circumstances, carded rounds of 69 and 71 respectively.

Woods, whose last win at Firestone came in 2009, said: ``I'm very pleased with that. I thought I hit it pretty good today and really controlled it. I missed a few putts in the 15-foot range, but overall a pretty good day.

“If you shoot something in the 60s here it’s always a good score but we have a long way to go. With the forecast, this course is supposed to dry out a little bit and get more difficult.”

World number three Rory McIlroy, US Open champion Justin Rose and Mickelson were among the later starters, with McIlroy one under after six holes and playing partners Rose and Mickelson one over and level par respectively after five.