He has a four-shot lead over fellow American Denny McCarthy, who fired a five-under 67, while Brendon Todd trails Bhatia by seven shots.
Japan’s Hideki Matsuyama moved into contention with a bogey-free round of 66, which featured six birdies, putting the 2021 Masters champion eight shots off the lead at seven under.
McIlroy, who is playing in his final tournament before the Masters next week, and Ryder Cup team-mate Tommy Fleetwood both had a frustrating day on Saturday – the Englishman also went round in level par in San Antonio.
Meanwhile, Sergio Garcia shot a four-under-par 68 to take a two-shot lead after the second round of LIV Golf Miami.
The 44-year-old Spaniard, who has yet to win a LIV Golf tournament, carded six birdies and two bogeys on his way to nine under.
England’s Tyrell Hatton is in joint second on seven under after a 67, which included six birdies and one bogey.
Jon Rahm, who will aim to defend his Masters title at Augusta National next week, is on five under going into the final round of the 54-hole event on Sunday.
