Stenson, bidding to win his first major at the age of 40, had five birdies and two bogeys in his three-under-par round to move to 12-under for the championship.
That gave him a one-stroke advantage over Mickelson, who had been in front after the first two rounds but was overtaken after shooting a one-under 70 to sit at 11-under overall.
Mickelson, the 2013 champion, had three birdies but dropped shots at the 14th and 17th cost him the lead and he only saved par at the last after finding himself in a greenside bunker.
It appears poised for a two-way shoot-out between them for the Claret Jug in Sunday’s final round with Bill Haas of the United States leading the chasing pack at six-under.
Haas shot 69, while England’s Andrew Johnston had a 70 and is fourth at five under par.
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