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.
Mickelson added a second round of 69 to his opening 63 at Royal Troon for a 10-under-par total of 132, one shot lower than the previous best at the Ayrshire venue set by American Bobby Clampett in 1982 and equalled by Darren Clarke in 1997.
And although that was only good enough for a one-shot lead over Sweden’s Henrik Stenson, Mickelson will be hoping of a repeat of the result at Muirfield in 2013, when he claimed his fifth major title as Stenson finished runner-up.
“We’re only halfway done with the tournament so it’s too far off to start thinking like that, but certainly there is nothing more than I would love to add another Claret Jug,” said the 46-year-old, who would become the fourth oldest winner of any major and the oldest in the Open since 1867.
“I think there is a lot of pressure off me given the fact that I’ve already got one.
“The other thing is that from 10 years ago, when I was playing my best golf, I’m 25 pounds lighter, I’m in better shape, I’m physically stronger than I was. I feel better and now that my swing is back on plane, I’m starting to hit some shots like I did 10 years ago and starting to play some of my best golf again.
“So I don’t see why there’s any reason why I can’t continue that, not just this week, but for years. That’s kind of what the game plan is.”
Mickelson had come agonisingly close to making history on day one, his birdie putt on the 18th to record the first 62 in any major championship catching the edge of the cup and staying out.
The resulting 63 was the 28th such score in majors and the first in the Open since Rory McIlroy’s opening round at St Andrews in 2010, which the Northern Irishman famously followed with an 80 in winds gusting up to 40 miles per hour which forced play to be suspended.
However, Mickelson was never in danger of suffering such a fate as a testing early breeze swiftly died and allowed him to extend his overnight lead to five shots with birdies on the fourth, seventh and eighth, the latter coming after his tee shot on the ‘Postage Stamp’ span back to within inches of the hole.
“That was really a salty little shot,” explained Mickelson, who wore a black all-weather glove on each hand to combat the intermittent downpours.
“I had a sand wedge and drove it back there to try and skid it back to the hole and you can see the delayed juice kick in.”
Wayward drives on the 12th and 15th led to Mickelson’s first bogeys of the championship and meant Stenson closed the gap to a single stroke thanks to a superb 65, his lowest score in the Open by two shots.
“I haven’t been in contention for the last six majors and it was a big, big goal of mine to try and be up there and give myself a chance. So far, so good,” the 40-year-old said.
“I’m not going to play these tournaments forever and ever. I don’t have another 50 goes at them. It might be a dozen or 15 in total so I better start putting myself in position and giving myself chances if I want to make it happen.”
Keegan Bradley famously won the 2011 US PGA Championship on his first appearance in a major and partnered Mickelson to four wins from five Ryder Cup matches in 2012 and 2014.
But after arriving in Scotland ranked 120th in the world, the 30-year-old decided the best way to get his name on the leaderboard was to put it there himself on Monday evening.
”I actually snuck up on the leaderboard on 18 with a couple of guys and we put our names up,” Bradley revealed after a 68 left him three off the lead alongside Denmark’s Soren Kjeldsen.
”I’m probably going to get in trouble for that and probably shouldn’t have said it. But it is fun to see my name up there next to Phil’s now. It’s just awesome.
“Because everyone’s wondering, I always get the question, ‘What’s wrong with you or something?’ And there’s nothing wrong. I’m just working. It may not happen this week but I know it’s going to. It’s feeling good.”
Defending champion Zach Johnson dropped two shots in the last four holes to finish five off the lead, a shot ahead of a five-strong group containing England’s Andrew Johnston and Spain’s Sergio Garcia.
Follow Day One of The Open LIVE with our leaderboard as the world’s best golfers vie for the third major of the year at Royal Troon.
Dustin Johnson, Jordan Spieth and Rory McIlroy again find themselves among the favourites to lift the famous Claret Jug. Check out all the developments from Day One below: