McIlroy opened strongly with consecutive birdies on the 11th and 12th holes to briefly take the solo lead before an eagle on the fifth moved him to three under par.
Two late dropped shots resulted in a one-under-par 69 for the world number two.
The Northern Irishman noted that his poor performance at the venue in 2018 prompted him to alter his major championship preparation by focusing on trajectory and short-game precision.
“I remember thinking to myself, I’ve got this backwards,” McIlroy said. “I should be in my comfort zone at Shinnecock and not here.”
Scottie Scheffler struggled on the 7,440-yard course, battling to a two-over-par 72 to remain six strokes behind the tournament leader.
“Overall it was a really challenging day,” Scheffler said.
“If you told me when I was staring at my par putt on nine that I would post two-over today, I would definitely have taken it at the time.”
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To prevent the notoriously difficult greens from drying out amid forecasts of 30 mph winds, the USGA took the unusual step of watering the putting surfaces during play.
