Stenson turned a one-shot overnight deficit into an identical advantage following a roller coaster day on Saturday that saw the final group separate themselves from the chasing pack and Rory McIlroy's patience snap - along with his three wood.
Looking to become the first male Swedish player to win a major, Stenson carded a third round of 68 to finish 12 under par, a shot ahead of playing partner Mickelson, who at 46 would be the fourth oldest winner of any major and oldest in the Open since 1867.
American Bill Haas was six shots off the lead in third, with England's Andrew Johnston - playing in only his third major - another shot back on five under.
After turning 40 in April, Stenson admitted time was running out in his bid for a maiden major, especially after failing to challenge in any of the last six and withdrawing from last month's US Open due to injury.
"This is a new opportunity and it would be massive to win the Open in Scotland," the Ryder Cup star said. "It's the one thing I am looking for and it would be the icing on the cake.
"I know Phil is going to keep on trying, he's a great competitor and one of the finest to play the game in the last 15 years. It's going to be tough, but I'm right where I want to be. I am going to stick to my game plan and hope it's enough when you add it all together.
"I've got two thirds and a second in the Open, I know what I want out of this week, but too many thoughts on the outcome is never good so I am going to try and stay on the mental plan I have and put in another good display.
"I was up there at Muirfield when Phil was a deserved winner, but there's always revenge. It would great to hand one back to him."
Three birdies in the first four holes took Stenson into the lead, only for the 40-year-old to three-putt the sixth and fail to get up and down from a bunker on the eighth, even though the famous Postage Stamp hole was playing just 100 yards as one of the changes made by tournament officials in anticipation of strong winds.
Mickelson had been left cursing the "golfing gods" after his birdie putt to shoot the first 62 in major history lipped out on Thursday, but received a massive stroke of luck on the 12th.
A badly sliced tee shot was headed deep into trouble but bounced off a gorse bush and into a position from where the left-hander was able to hack out down the fairway.
Mickelson's approach to the green then span back around 15 feet and caught a down slope that took it closer to the hole, from where he holed for the most unlikely of pars.
A birdie from 25 feet on the 13th doubled Mickelson's advantage, but the 46-year-old lost it immediately by three-putting the 14th after Stenson had holed from four feet for birdie.
Mickelson went back in front with a birdie on the 16th, but there was time for another two-shot swing on the next, Stenson holing from 15ft for birdie and Mickelson making bogey after a wayward tee shot.
World No19 Mickelson, who would join Lee Trevino and Nick Faldo with six major titles with victory on Sunday, said: "It's a great opportunity and a great challenge.
"I was off (on Saturday), I didn't have my best stuff and I was a little bit short of my rhythm. It could have been a day that got away from me, but I'm pleased I found a way to shoot under par and kept myself in it."
McIlroy had not given up hope of securing a second Open title despite starting the day eight shots off the lead, but never threatened to make a charge after carding three bogeys in the first five holes.
And the four-time major winner's frustrations finally came to a head on the 16th as he hurled his fairway wood to the turf and saw it snap into pieces after a wayward approach to the par-5.
''The clubhead came loose on it earlier in the week so I had to get it re-glued, so it is partly to do with that and partly the throw itself,'' said the 27-year-old, who said last year's fine for launching his three iron into a lake at Doral during the WGC-Cadillac Championship was reduced from $25,000 US to $5,000 for apologising on TV.
''I let one go right on the previous hole, a three iron, and I did the same thing there. It was basically a bad swing.''