Berger, who has not won on the PGA Tour since 2021, put himself on course for the £3m top prize thanks to a clean run on the back nine which included three birdies.
“I actually feel like I played better [today] – the course was a little tougher,” he said.
“I’m looking forward to the next couple of days and seeing the challenge they bring.”
Americans Sahith Theegala and Collin Morikawa and Sweden’s Ludvig Aberg are tied for third on seven under, with American Ricky Fowler one shot further back.
McIlroy, who birdied four of the first seven holes on the back nine, said: “I played the last 10 holes really, really well.
“Overall I am really pleased. I played a very sort of controlled, patient round of golf, which you need to do around here.”
American world number one Scottie Scheffler bogeyed the 18th in a round of 71 that left him three under.
England’s Tommy Fleetwood, who was four over after the first round, shot three birdies on the back nine in a second-round 69 to make the cut on one over.
