Mickelson was in a group of four players in a tie for second after making six birdies in his final 11 holes for a 66 on Saturday. His performance has the American talking up his improving links game before next week's British Open.
Stenson, at 16 under for the tournament, has emerged from a prolonged slump and is showing the kind of consistent form that took the Swede to No. 4 in the world four years ago.
"I wouldn't say I'm far off that," said Stenson, who was as low as No. 230 in the rankings 18 months ago. "The way I played today, that was top-10 standard. It's as good as I have hit the ball all season."
With the wind arriving late in the day and the sun again beating down, Castle Stuart was largely defenseless for a third straight round. But no one could pull away.
Chris Doak was the overnight leader but seemed to feel the pressure to become Scotland's first home winner in 14 years. He shot 73.
Accurate off the tee and creative as ever around the greens, Mickelson chose the ideal day to show off his full repertoire of skills.
American television was broadcasting a regular European Tour event live for the first time this weekend, with NBC fortunate enough to have Mickelson in contention.
The four-time major winner had four birdies in five holes playing into the wind. A delicate chip to within three feet set up another birdie at No. 16, and a 15-foot putt on the final hole lifted him briefly into the lead and drew one of the biggest cheers of the day.
"The last 11 holes were a lot of fun for me to play," he said.
Mickelson is seeking his first win in Europe in 20 years and first in Britain. That would prove the ideal way to go into the British Open.
"I have kept the ball in play as well as I ever have [on links]," said Mickelson, who found 11 of 14 fairways on the undulating course in the Scottish Highlands.