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"I played the last 10 holes really, really well," said McIlroy, who birdied four of the first seven holes on the back nine.
"Overall I am really pleased. I played a very sort of controlled, patient round of golf, which you need to do around here."
The most recent of Berger's four PGA Tour titles came in 2021.
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.
