Curtis, who came into the day with a two-stroke advantage, finished it with a three-shot advantage at the AT&T Oaks Course at TPC San Antonio.
He finished 54 holes at 9-under-par 207, three clear of Matt Every, who also carded a 73 to slip into sole possession of second place.
John Huh fired a 5-under 67 to jump 37 places and pull into a third-place tie with Charlie Wi (71) and Seung-yul Noh (68) two shots further back at minus-4.
Matt Kuchar (67) matched Huh for best round of the day and jumped into a sixth-place logjam with Brian Gay (71), Greg Chalmers (69), David Mathis (77) and Cameron Tringale (76) at 3-under 213.
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