Early starter Harman landed a barrage of birdies on his front nine and then eagled the 18th to post a six-under 65 that left him out on his own at 10 under.
England's Tommy Fleetwood, one of three overnight leaders after first-round 66s, was given huge support but struggled to make inroads and was five behind with two holes to play.
Austria's Sepp Straka emerged as a weekend contender for the Claret Jug with six birdies on a sizzling back nine in a second-round 67 to move to four under.
Australian Min Woo Lee (68), compatriot Jason Day (67) and India's Shubhankar Sharma (71) were in a group on three under.
Several players threatened to make an afternoon charge but the links course alongside the Dee Estuary was in a miserly mood with the greens devilishly difficult.
American Jordan Spieth, the 2017 champion, birdied three of his first six holes but struggled on the back nine and ended up going nowhere with a level-par 71 to stay on two under.
HOT PUTTER
While it was a day of hard graft for the majority, Harman, who finished in a tie for sixth at St Andrew's last year, made a mockery of the tough scoring conditions with his putter red-hot.
"I've had a hot putter the last couple of days so try to ride it through the weekend," Harman, who has only two career victories on the PGA Tour, told reporters.
"Last few weeks I found a little something on the greens that I felt like gave me a little better roll."
The left-hander got on a roll with a birdie at the second, third and fourth and then almost chipped in for an eagle on the fifth before tapping in another birdie.
Harman kept the momentum on the back nine with a sensational chip-in from off the green at the par-four 12th to avoid a bogey before putting the icing on the cake with a brilliant approach to the par-five 18th before nailing his eagle putt.
He needed only 23 putts for his round and if his stroke remains as steady at the weekend he will be hard to catch.
Harman did hold the 54-hole lead at the US Open before finishing second but, if he is looking for omens, the last two winners at Hoylake - Tiger Woods in 2006 and Rory McIlroy in 2014 - were also on 132 after two rounds.
McIlroy arrived this year as pre-tournament favourite but he suffered more frustration with his putter, managing to improve only one shot from his first-round 71 to sit nine behind Harman.
South African amateur Christo Lamprecht came down to earth with a bump after sharing the overnight lead. Following a first-round 66, he slumped to an error-strewn 79 but just about made the cut for the weekend.
Argentina's Emiliano Grillo, the other first-round leader, also dropped back after a three-over 74.
HUGE GALLERIES
Just as on Thursday, huge galleries lined the fairways, and as well as watching the golf they saw Just Stop Oil protesters briefly halt play at the 17th with orange flares and powder.
Security staff quickly removed the individuals with the help of American Billy Horschel and there was no damage.
McIlroy gave his fans early encouragement by rolling in a birdie putt at the testing par-four opening hole and a superb rescue from a green side bunker at the fifth earned him another.
He dropped his first shot of the day at the 11th, missed a birdie at the 12th before making a superb up-and-down from a bunker at the 13th to stay below par.
A six at the 15th was cancelled by a birdie at the 18th but it was a frustrating day for the four-time major champion.
"Right now it's out of my hands, but at the same time, I think if I can get to minus three, four, five under going into Sunday, I'll have a really good chance," McIlroy said.
"It played really, really tough today."
Playing partner Jon Rahm, the Masters champion, made the weekend with a battling one-under 70 to sit at two over while US Open champion Wyndham Clark shot a 73 to stand one-under.
Defending champion Cameron Smith eagled the 18th to squeeze inside the cut line while world number one Scottie Scheffler's birdie at 18 also spared him an early exit.
Several former Open champions will be missing at the weekend though, including Phil Mickelson, Shane Lowry, Collin Morikawa and Francesco Molinari.
Australia's Travis Smyth earned the loudest roar of the day with a hole-in-one at the 17th although at eight over and with the cut likely to be three over he will miss the weekend.
