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But a six-under 65 from Henrik Stenson left the Swede only one shot behind.
Denmark's Soren Kjeldsen (68) and American Keegan Bradley (68) are three shots off the lead, two clear of defending champion Zach Johnson (70).
Northern Ireland's Rory McIlroy shot 71 in the worst of the weather to finish eight shots off the pace.
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Andrew Johnston is the highest-placed Briton on four under, the Englishman recovering from a triple bogey at the fearsome 11th to record an impressive 69.
Meanwhile, Germany's two-time major winner Martin Kaymer got to seven under but triple bogeyed the 10th and finished with a 73 for three under.
The wind blew harder and the rain fell heavier after Mickelson reached the safety of the clubhouse, destroying the chances of a host of big names.
World number three Jordan Spieth shot a 75 to finish right on four-over-par and just make the cut, as did England's Masters champion Danny Willett, Northern Ireland's Graeme McDowell, and Scottish duo Colin Montgomerie and Paul Lawrie.
England's former US Open champion Justin Rose shot a 77 to finish three over, while world number one Jason Day battled to a 70 to finish one over.
US Open champion and world number two Dustin Johnson had two double bogeys but still managed a 69 for two under overall.
World number five Bubba Watson holed a birdie at the last to extend his stay. The two-time Masters champion double-bogeyed 11 and struggled to a 76 and four-over total.
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Mickelson, winner of the Claret Jug in 2013, carded a 63 on Thursday, the joint-lowest round in major history and the 46-year-old's 36-hole total of 132 is a record for an Open at Royal Troon.
The five-time major winner told BBC Sport: "If I look back to my mid-30s, I am 35lbs lighter, in better shape than I was and can manage the symptoms of my psoriatic arthritis. I feel stronger and in a better condition than I have ever been.
"I can't see why I can't play my best golf in the coming years. I am optimistic about this week and the coming years and the opportunities to add to my resume."
Mickelson teed off in overcast but benign conditions and covered the front nine in 33 shots, very nearly acing the eighth hole.
It started to rain when he hit the turn and he dropped his first shot of the tournament at the par-four 12th, but ground things out as others wilted.
Mickelson's feats were brought into sharper focus by the efforts of playing partners Lee Westwood and Ernie Els, who started their rounds on level par.
England's Westwood carded a 73, while two-time Open champion Els shot a five-over 76 and missed the cut by one shot.
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World number six Stenson, runner-up to Mickelson in 2013, made six birdies and one bogey as his attempt to become the first Scandinavian to win a major title gathered momentum.
"I haven't been in contention for the last six majors so it was a big goal of mine to give myself a good chance here. So far, so good," said Stenson.
"I'm 40, so might only have another dozen goes. So I better start putting myself in position and giving myself chances."
The affable Johnston, winner of the Spanish Open in May, is a developing something of a cult following. Johnston is nicknamed 'Beef', which prompted fans to wave burgers at him as he made his way from the 15th green.
"My mum, sister and niece are here," said the 27-year-old Londoner.
"My niece is five. I can hear her shouting out 'Uncle Beef' on every hole. Today she came out with 'Beef to the rescue!' She cracks me up."
Johnston is tied for sixth with Americans Tony Finau (71) and Bill Haas (70), former Masters champion Charl Schwartzel (66) and Spain's Sergio Garcia (70).
South Africa's 2010 champion Louis Oosthuizen had five bogeys, a double bogey and a quintuple-bogey nine in a humbling round of 83.
Ben Curtis, Open champion in 2003, recorded a sextuple-bogey 10 at the par-four fourth, hitting his ball into three different bunkers. He also shot an 83.
The last two champions at Troon, Todd Hamilton and Justin Leonard, also missed the cut after finishing six over.
There is a slight silver lining for those blown off course on Friday afternoon, with the news the early starters will get the better of the weather on Saturday.
It is forecast to be cloudy but mostly dry in the morning, with the odd bright spell, but the wind is set to get up in the afternoon, with showers also expected.
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American Phil Mickelson leads the Open Championship at the halfway stage, a two-under-par 69 lifting him to 10 under at Royal Troon.