Cauley, ranked 1,258 in the world, is making only his second PGA Tour appearance since September 2020, after suffering injuries in a vehicle accident in 2018.
A bogey-free 65 at PGA National put the 33-year-old at 11 under.
McIlroy, the world's number two, shot a second straight four-under-par 67 to reach eight under.
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