Tournament host Tiger Woods and U.S. Open champion Geoff Ogilvy share second place at 4-under-par 68.
Stenson trailed the leaders most of the day, but a late surge on the back nine at Sherwood Country Club gave him the first-round lead.
Ogilvy was atop the leaderboard most of the first round before Stenson pulled through in the end. Ogilvy opened with birdies on one and three, but dropped a stroke on the second.
The Australian carded three more birdies on the front side to make the turn atop the leaderboard in minus-4. Ogilvy climbed to 6 under with a birdie at 13 and a 12-foot birdie putt at the 17th.
However at the par-4 18th, Ogilvy missed the green right and had a terrible lie. He hit his third shot about 3 feet before pitching his fourth to 20 feet. Ogilvy two-putted from there for double-bogey which dropped him to minus-4 and a share of second with Woods.
'I played fairly well. I birdied the first hole and bogeyed the second, and after that it was pretty good, for the next 15 holes,' Ogilvy said. 'I hit it quite nicely, had a few bad shots I guess on the back nine, but I was chipping very well. I hit it in a bad spot on the 18th and made a double, which was annoying.'
Woods birdied the first and got to 2 under as his 8-footer for birdie at the fourth found the bottom of the cup. He came right back with a two-putt birdie on five.
The 30-year-old parred five straight before draining a five-foot birdie putt on 11 to tie Ogilvy in the lead at minus-4. Woods fell back to minus-3 with a bogey on 15. He rebounded with a two-putt birdie on the par-5 16th to share second.
'I had two careless three-putts. I really didn't have control on the speed of the greens at all,' Woods admitted. 'I made a lot of came-backers and left some short. It was kind of a struggle on the greens.'
Stenson meanwhile was biding his time. He collected his only front-nine birdie on the par-3 second. Around the turn, Stenson birdied Nos. 10 and 13 to move to minus-3.
The Swede flew up the leaderboard from there. Stenson converted a birdie try on the par-3 15th and made two straight as he birdied 16. He capped a run of three straight birdies at the 17th as he sank a 12-foot putt.
All of a sudden, Stenson was in the lead thanks to Ogilvy's double-bogey at the last. Stenson two-putted for par from 15 feet at the last to maintain the first-round lead.
'I just changed equipment about three weeks ago and finished second in Sun City and I'm having a a good start here,' said Stenson, who won twice on the European Tour in 2006. 'I played a lot last week at the World Cup, so things are going good.'
Two-time Masters champion Jose Maria Olazabal opened with a 2-under-par 70. He was joined in eighth place by Chris DiMarco.
David Howell is the final player in red figures at minus-1. Defending champion Luke Donald struggled to a 4-over-par 76 and is alone in 15th place out of 16 golfers.