Sweden's Stenson leads long-time leader Mickelson by one stroke at 12 under with a five-shot cushion back to nearest chaser Bill Haas of America going into the final day.
Stenson, 40, an accomplished Tour winner, former world No. 2 and three-time Ryder Cup star, is bidding to become the first Scandinavian man to win a major title.
Mickelson, 46, is chasing a sixth major title and first win since clinching the Open at Muirfeld in 2013.
The tussle at Troon on a blustery, mizzly Saturday was reminiscent of the famous "Duel in the Sun" Open featuring Jack Nicklaus and Tom Watson down the road at Turnberry in 1977. Except in worse weather.
Mickelson led by one starting out but Stenson quickly joined the American as co-leader at the first hole and by the fourth was clear on his own.
It was like the maverick against the machine. Mickelson was erratic off tee and fairway, but scrambled time and again to save par. Stenson was cool and metronomic, gently applying the pressure.
But then the machine broke down.
"So he is human," muttered a Scots voice in the crowd beside the sixth green as the Swede missed a tiddler for par.
Mickelson had to come into the green from beyond a TV tower in the left rough, but for "Lefty" it comes with the territory and he made another par the hard way. You can't be swashbuckling if you don't buckle now and again.
"I was off today. I didn't have my best stuff," he said. "My rhythm was a little quick and I was jumpy. It could have been a day that got away from me, instead I shot under par and kept myself right in it so I'm proud of that. "
By now the spectators sensed there was only one game in town and the galleries around the last group swelled to final-day volume. In size and audio levels.
Mickelson is the crowd-pleaser, for past deeds and his engagement with the people. Flashing that ice-white grin, making eye contact and giving thumbs ups, while handing used balls to kids behind the ropes endears him to multiple generations.
Stenson is a lesser-known quantity to the public -- although privately deadpan funny -- but as a three-time European Ryder Cup player he had plenty of followers.
Asked how he rates his chance, he said: "I give myself a 50-50, it might happen, it might not happen. The sun will come up on Monday anyway, hopefully. Maybe not in Scotland, but in other parts of the world."
By coincidence victory for Stenson would also reverse the fortunes of 2013 at Muirfield when Mickelson came past at a clip in the final round to win his first Claret Jug and fifth major.
"It would be great to hand one back to him," said Stenson, when reminded of the occasion afterwards.
The maverick turned the tables on the Postage Stamp short eighth, catching the fringe with his tee shot as Stenson's ball plunged into the front bunker. A par to a bogey put the American back in front.
More driving trouble for Phil on the 12th as his tee shot ran through the fairway into a gorse bush. He hacked out and his approach span back sufficiently close to make his par putt. Mickelson let out an audible "Phew". He knew it was a big one.
"Some days it's easy and it looks pretty like the first couple, and some days it's hard and looks terrible like today but either way I shot three rounds under par," he said.
The Californian ramped up his celebrations a notch with a big uppercut fist pump when his first birdie of the day dropped on the 13th to grab a two-shot lead.
But like boxers landing scoring punches they traded the lead again until by 18 the robot had fully rebooted to sit atop the leaderboard.
Mickelson dismissed the notion that Sunday would be a straight head-to-head, although Stenson suggested he would have one eye on the American, one on the course.
"I enjoy his company," he said of his rival. "He's always fun to watch. He hits some spectacular shots and he's a great competitor. So it's inspiring. I know I'll have to bring my best. I don't necessarily feel that much pressure. It's a great opportunity. I've got my gameplan."
However, history shows the chasers could still have their say. After all, Scotland's Paul Lawrie famously came back from 10 behind on the final day at Carnoustie in 1999.
Haas, winner of the PGA Tour's season-long FedEx Cup in 2011, is trying to do something his nine-time Tour winning father Jay couldn't and win a major. He also fits the Troon champion profile -- the last six winners here have been American and the last three first-time major winners.
One further back is Englishman Andrew Johnston, known as "Beef" on account of his ample girth. His Amish-style beard is another distinguishing feature. The 27-year-old clinched his first European Tour title this season but is only playing in his second Open and third major in total after missing the cut in 2011.
Out of the top 15 players, Mickelson, Charl Schwartzel and Keegan Bradley at two under and U.S Open champion Dustin Johnson at one under are the only major winners. Johnson got it to five under to challenge, but triple-bogeyed the 11th.
The sun may not come out, but the engraver has a fairly good idea of the last three letters of the name for the Claret Jug.