The 36-year-old Swede, without a victory for more than three and a half years, takes a three-stroke lead into the final round after responding to George Coetzee's course-record 63 with a 69 to reach 16 under par.
Stenson's push came after Ian Poulter charged into a one-stroke lead over Adam Scott in Australia, Luke Donald went four clear in Japan and Miguel Angel Jimenez moved into a share of top spot at the Hong Kong Open.
South African Coetzee gave himself another chance of a first European Tour title with an eagle two and nine birdies, but the 26-year-old from Pretoria also had bogeys at the 12th and 15th.
Stenson, already three clear at halfway, had a hat-trick of birdies from the seventh and, after a three-putt bogey at the 10th, hit back with a two for the third day running on the 183-yard 15th. Driving into sand led to a six on the long 16th, but a superb chip from the rough at the 17th gave him a sixth birdie of the round.
Compatriot Magnus Carlsson birdied the last for a 68 to tie with Coetzee in second place, while Darren Fichardt – another of the home contingent – is fourth, three strokes further back.
Lloyd Saltman's unlikely bid for victory to make the European Tour next year came unstuck with a three-over 75 which dropped him from fourth to 20th, with a 211 total. Fife's Peter Whitehead was one shot ahead after he continued his steady progress with a level-par 72. Marc Warren was on the same score after a 71, but Craig Lee had a bad day, shooting a 77 to be in a tie for 38th; however, at 116th on the Order of Merit, he may have already done enough to qualify.
Michael Campbell survived two major scares at the Hong Kong Open, but the New Zealander remains on course to end a seven-year title drought.
The 43-year-old started the third round with a one-stroke lead and, after scrambling to shoot a one-under-par 69, he was joined at the top of the leaderboard by Spain's Jimenez on 10-under for the tournament. Campbell last won in 2005, when he followed up his US Open triumph with the World Match Play Championship title. At the 10th hole, he struck his ball a few yards while preparing to tee off but he was able to replace it without penalty after referee John Paramor accepted he had not intended to play a shot. At the 18th he found a greenside bunker with his approach but holed a 20-foot par putt to maintain a share of the lead.
"What happened on the 10th was hilarious," Campbell said. "I haven't done that since I started playing 38 years ago. But I knew it was not a penalty and when John Paramor started walking towards me with a smile on his face, I knew I was fine."
If Jimenez does win today, he will become the oldest player to claim a European Tour victory, at the age of 48 years and 318 days.
However, Campbell and Jimenez face a final-day challenge from Italian Matteo Manassero, one shot off the pace after a third-round 64. Last Sunday he became the first teenager to win three times on the European Tour, with victory in the Singapore Open in a play-off.
Scotland's Stephen Gallacher shot his third 68 to sit joint eighth, four shots off the lead, with compatriot Paul Lawrie one shot further back after a 67.