Down near the rear of the field after an opening 77, Stenson went to the turn in 31 on his return to the Doha course and was only four behind leaders Thomas Aiken and Retief Goosen.
After birdies at the 14th, 16th and short 17th, the 2006 champion eagled the 589 yard last before heading over to the front nine.
With overnight leader Goosen among the later starters, his fellow South African Aiken grabbed the opportunity to move alongside him on three under par by adding birdies at the second and seventh to his opening 71.
England's former Ryder Cup star David Howell was another going well, hitting back from his first day 75 with four birdies in seven holes around the turn to climb to one under.
But Martin Kaymer and Paul Casey, the winners of the first two events on the Desert Swing, were deep in the pack.
Casey followed a birdie on the 11th with bogeys at the 13th and 15th to be three over and playing partner Kaymer, needing a top-two finish to have a chance of toppling Lee Westwood as World Number One, was four over.
The halfway cut was likely to be around the five over mark.
Aiken, chasing his first European Tour title, had to wait until the long 18th for another birdie, but by keeping a bogey off his card in the calmer conditions he was in with a 69 and four under aggregate.
"It was a lot less windy and there were no gusts like yesterday," he said. "That made it a lot easier to get round the course.
"I missed a few with my putter, but I was very consistent and that's the name of the game."
The 27 year old was one ahead of Goosen, yet to tee off again, while former Open Champion - and former Qatar winner - Paul Lawrie joined the group on two under with five still to play.
Kaymer was close to a hole-in-one at the third and improved further to three over, but Casey, having repaired some of the earlier damage, got a flyer over the green on the fifth and double-bogeyed to go back to five over.
Stenson was unable to extend his sparkling run and a three-putt bogey at the sixth saw him slip to one over, while Howell's 69 meant he reached halfway on level par.