Mickelson was in a group of four players in a tie for second after making six birdies in his last 11 holes for a 66 on Saturday. His performance has the American talking up his improving links game before next week's British Open.
Branden Grace and first-round leader John Parry were tied with Mickelson after each shooting 66, along with J.B. Hansen (69).
Stenson 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.