After 12 holes, the American world number nine led by one shot at six under after a low-scoring start to the tournament at Erin Hills in Wisconsin.
Fowler, 28, who is chasing his first major victory, reeled off three birdies in his opening five holes after teeing off on the par-four 10th.
He then notched a hat-trick of birdies on the 18th, first and second holes to drop to six under.
England's Tommy Fleetwood was in hot pursuit, with five birdies to be at five under after 12 holes.
But world number one Dustin Johnson endured a torrid start to the defence of his title with a double-bogey and two bogeys on the front nine.
Masters champion Sergio Garcia and Northern Ireland star Rory McIlroy tee off later Thursday.