The popular Johnston, inspired by the fans crying out his nickname 'Beef, Beef' at almost every hole, ended up on 208, one ahead of American JB Holmes (69).
Stenson made his intentions clear when he birdied the opening hole. He then went one ahead of his playing partner after picking up another shot at the fourth.
A bogey at the sixth dented the Swede's hopes before 2013 Open champion Mickelson had a stroke of fortune at Troon's signature eighth hole when his tee shot at the Postage Stamp seemed destined for a trap before spinning back and avoiding the bunker.
Stenson was not so lucky, his effort did find sand and he bogeyed again. Mickelson then rolled in three nerve-tingling putts at the 10th, 11th and 12th to keep in front before ramming in a 25-foot birdie effort at the 13th to go two clear.
Stenson, though, came battling straight back to level matters at the 14th, delivering a laser-guided approach to six feet and holing out for birdie while his title rival's three-footer for par lipped out.
Seemingly undeterred, Mickelson rallied by coaxing in a seven-foot birdie putt at the 16th before the pendulum swung again a hole later when his playing partner knocked in a 20-footer for birdie to reclaim the lead.
There was yet more drama when Mickelson had an angry exchange with a photographer after finding sand with his approach at the last.
The short-game master, however, conjured some typical late magic to end one behind Stenson.