Horschel, who had to survive the qualifying tournament late last year to retain his playing privileges on the PGA Tour, has made the cut in all 10 of his starts in 2013.
He finished tied for second behind winner D.A. Points last week at the Houston Open and has put himself in position to win his first tournament on the circuit.
Horschel shot his second straight 4-under-par 68 at the TPC-San Antonio Oaks Course and his 136 total gave him a two-stroke lead over Daniel Summerhays, Charley Hoffman and Stephen Bowditch.
Among those tied for fifth at 139 was Rory McIlroy, the world's second-ranked player who shot a 5-under 67 that included two bogeys.
There were 28 players within five shots of the lead heading into the weekend of what is the final tournament prior to the playing of the Masters. A win this week would earn Horschel an invitation to that event.
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