Stenson added a second round of 69 to his opening 64 at Bay Hill to set the early clubhouse target on 11 under par, a target matched minutes later by American Bryson DeChambeau following a 66.
Rory McIlroy, who has missed the cut in two of his last four starts on the PGA Tour, is six shots off the pace after a second round of 70 which featured five birdies and two bogeys.
Stenson had covered the back nine in 31 on Thursday, but after starting the second round from the 10th, the former Open champion could only manage nine straight pars to reach the turn in 36.
The par streak was extended to 13 holes before Stenson found his range on the greens to birdie the fifth, sixth and seventh to maintain his bid for a first win of the season.
Asked what made the difference between missing the cut in last week’s Valspar Championship and his performance so far, the world number 15 told PGA Tour Live: “Putting more than anything, but a combination of putting and my shots.
“I’ve been hitting a few really close this week and setting up some good opportunities from three or four feet. Today wasn’t as good as yesterday, obviously but the important part for me was 16, 17, 18. I scrambled for par all those three holes after hitting some not so-good golf shots.
“I kept patient and then I got on a strong and made three [birdies] in a row coming home. Three under around this golf course is never bad.”
McIlroy’s putting was noticeably better than in recent weeks and the four-time major winner told Sky Sports: “That’s been a huge improvement over the first two days. I sort of messed around on the putting green a little bit, trying to go back to some feels I’ve had before and putted really well. Hopefully that continues. Over the weekend last year I was hitting driver pretty much everywhere, leaving myself wedges in. If I drive it like that again over the weekend I feel like I’ll have a good chance.”
McIlroy shot rounds of 65 and 69 last year to finish in a tie for fourth, two behind winner Marc Leishman.