He began the day one stroke behind the three-way leaders but moved three clear on eight under after birdies at the second, third, fourth and fifth holes.
It could have been even better for the left-hander as his chip from off the green at the fifth struck the flag and almost dropped in for an eagle.
The rock-steady Harman then made four successive pars to reach the turn in 31 strokes.
Of the overnight leaders on five-under after first-round 66s, Argentina's Emiliano Grillo dropped back after a double-bogey at the second and a bogey at the third.
Local favourite Tommy Fleetwood and South African amateur Christo Lamprecht, who shared the lead with Grillo, were teeing off their second rounds later.
Just as on Thursday, large galleries lined the fairways alongside the picturesque Dee Estuary, many of them watching pre-tournament favourite Rory McIlroy.
The Northern Irishman gave them something early to cheer by rolling in a birdie putt at the testing par-four opening hole, moving him to one under for the championship.
McIlroy, bidding to emulate his 2014 victory at Hoylake and claim a long-awaited fifth major, had a great chance of another birdie at the third but missed a four-foot putt.
Conditions were proving difficult with McIlroy's playing partner Justin Rose going out of bounds at the third on his way to dropping a shot to slip to five-over.
Masters champion Jon Rahm, also playing with McIlroy, began with four pars but needs to make up ground at three over.
England's Matthew Southgate, playing in the first group of the day, took the early clubhouse lead on one-under after an eagle at the 18th hole.
Defending champion Cameron Smith (one over par) begins his second round just before 3 p.m.
