Horshel also came into the day with two-stroke lead and turned in a steady round in a bid for a his first PGA Tour title and a spot in next week's Masters.
He finished 54 holes at 10-under-par 206 at TPC San Antonio.
Horshel birdied the 14th from five feet out, moving to minus-11, then faltered to a bogey at 15th to slip back to 10-under, where he stayed following three pars to close out the round.
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