Harman ended the second round with a 13-under 127 total to head a group of five players, including twice major champion Zach Johnson, at 10-under. Defending champion Justin Thomas posted a second straight 67 to trail by seven.
Harman, a two-time PGA Tour winner, says his game has reached a new level since he switched to a new ball in May.
"It's made a huge difference," he told reporters. "I wasn't a very good wind player. When I switched I was 90th in the world.
"I won the first week I put (the new ball) in. I'm able to flight the ball so much better than I used to. I feel like I was a better ball striker when I was a kid than a pro. I'm starting to get those feelings back."
Harman, now ranked 23rd in the world, is sixth in the American Ryder Cup standings, well in contention for one of 12 spots on the visiting team for the October competition against Europe outside Paris.
Spieth, a certainty for that team, endured a frustrating day on the greens on Friday, with the exception of the fifth hole.
After leaving his approach shot a little more than 90 feet away, Spieth struck his birdie putt more in hope than expectation, but misjudged the pace.
His ball seemed destined to scuttle well beyond the hole, which fortunately got in the way and acted as a backboard, the ball disappearing for an unlikely birdie with the PGA Tour confirming it was his longest successful putt on the circuit.
Spieth, however, was not happy with his overall display.
"I'm trying to get real comfortable on the greens, and that's a concern," he said after signing for a 68.
"I had to play a little conservative towards the end of the round today to make sure we're getting to the weekend."
The cut survived, Spieth plans to attack, with a 72-hole total of 16-under in mind.
"Now we can fire away," he said.
(Reporting by Andrew Both in Cary, North Carolina; Editing by John O'Brien)
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