The left-hander, world number 26, was among the early starters at a cold and windy Hoylake after his opening 67 and he plundered four successive birdies from the second hole.
Harman followed up with 12 pars in a row, including one saved with a chip-in from a bunker, before a spectacular eagle at the 18th lifted him to 10 under, five ahead of overnight leaders Tommy Fleetwood, Christo Lamprecht and Emiliano Grillo.
"I've been hitting a lot of fairways and then I've been hitting it on to most of the greens and I'm putting well," Harman told a news conference.
"I am delighted with how I'm playing. I've had a hot putter the last couple days so am going to try to ride it through the weekend."
Harman, a twice PGA Tour winner, missed the cut in four of his first five Open appearances but finished tied sixth at St Andrews last year.
He was also joint second at the 2017 U.S. Open, an experience he believes he has learned from.
"I think when I held the 54-hole lead at the U.S. Open, I just probably thought about it too much," he said. "Just didn't focus on getting sleep and eating right. So that would be my focus this weekend."
Harman is a keen hunter and fisherman back home in Georgia and he likens the challenges to those of playing links golf.
"I've been a hunter my entire life," he said. "I enjoy the strategy of it. I like links golf. There's several different options to play golf holes. I enjoy the variety of shots you have to hit."
