Stenson eagled the 13th hole and charged into contention at the wind-swept Old Course.
The Swede, who won the biggest title of his career at last year’s US PGA Players Championship, fired four birdies on his outward nine as well and stands joint fourth on eight-under par.
Brisk winds that ripped apart rounds Friday returned to the legendary links to wreck more dreams.
“It wasn’t as bad, but it really picked up. The gusts are extremely strong,” Stenson said. “It’s feels like the wind is trying to rip your pants off and that’s not a good thing.”
Stenson was hopeful of becoming the first Swedish man to win a major after a history of women’s golf success led by retired star Annika Sorenstam.
“It’s going to be a lot of guys fighting it out for this one, but we have been longing a long time,” Stenson said. “To have a Swedish male player win a major, if it could happen tomorrow, that would be great.”
South African Louis Oosthuizen off a challenge from England’s Paul Casey and seized a four-stroke lead after Saturday’s third round of the British Open at the wind-swept Old Course.
Oosthuizen, who missed the cut in seven of his eight prior majors, birdied two of the last three holes to fire a three-under par 69 and stand on 15-under 206 through 54 holes at the legendary links course.
Casey, hoping to be England’s first major champion since Nick Faldo at the 1996 Masters, fired a five-under 67 to stand second by four strokes with Germany’s Martin Kaymer another three strokes adrift in third after a 68.
With Oosthuizen stretching his margin with a 40-foot birdie putt over a ridge at the 16th and a tap-in birdie at 18, Kaymer made it clear he saw little hope for those behind him.
“Too far away would be probably seven, eight shots,” Kaymer said. “I don’t really see myself shooting a 63 under those conditions and I’m not expecting them to shoot 73 or 74.”
Not since American Tony Lema in 1964 has a first-time major champion been crowned at the birthplace of golf, but such a fate seemed assured Sunday.
Two-time US Open winner Retief Goosen of South Africa was the only prior major winner in the top 17.
England’s third-ranked Lee Westwood, this year’s Masters runner-up and third in the two majors before that, shared fourth on 209 with Stenson and Spain’s Alejandro Canizares.
American Dustin Johnson was seventh on 210, one stroke ahead of countrymen Nick Watney, Ricky Barnes and Sean O’Hair as well as Goosen.
Northern Ireland’s Rory McIlroy, Spain’s Sergio Garcia and South Korea’s Jin Jeong, who won last month’s British Amateur to qualify for the Open, were among six players on 212.
World number one Tiger Woods, a 14-time major champion seeking his first title since a sex scandal last November destroyed his iconic image, struggled to a one-over par 73 to share 18th on three-under 213 with 18 holes remaining.
Woods, chasing the record 18 majors won by Jack Nicklaus, won British Open titles in 2000 and 2005 at the Old Course but appeared to have no chance this year at becoming the first three-time Open winner at St. Andrews.
Kind pin placements by the Royal and Ancient Golf Club cracked the door for a run at the lead which only Casey nudged wipe open.
“The only difference was probably the pin positions,” Kaymer said. “They were a little bit more generous, so thanks to the RandA there.”
Casey had five birdies on the front nine, twice moving within a stroke of the lead only to have Oosthuizen answer each time with a birdie.
Oosthuizen, a 27-year-old former farmboy mentored as a teen by three-time major winner Ernie Els, began with a bogey but birdied seven and nine to deny Casey’s challenge.
Casey, who broke a US collegiate scoring mark set by Woods in 2000, has never managed a top-5 finish in 29 prior majors.
Woods battled at level par for the day until finding the namesake pavement of the Road Hole at 17 and taking a bogey. Woods gave himself his fourth eagle putt of the round at 18 but three-putted for par.
Woods, who ditched a putter he had used since 1999 for a new brand this week, struggled on the greens but said it had nothing to do with the putter.
“I just need to have better speed,” Woods said. “I hit it good. I just didn’t get anything out of the round. I couldn’t build any momentum, wasn’t making any putts.”
McIlroy, who matched the low round in major history with an opening 63 but soared to an 80 in gusting winds Friday, came back with a three-under par 69 to stand at four-under 212 for 54 holes.
“It was great to come out and play nicely,” McIlroy said. “I felt as if I responded quite well to the way everything happened. I’m not going to let one round of golf really get me down.”
McIlroy made five birdies in the last 11 holes but took a double bogey at the Road Hole.
“I hit a good shot on 17, just got a gust of wind that completely switched it,” McIlroy said. “It was pretty unfortunate, but that’s links golf and you’ve just got to deal with it.”