Curtis made four birdies in his first nine holes of the round on the back nine of the AT&T Oaks Course at TPC San Antonio en route to the lead. The 2003 British Open winner is seeking his first PGA Tour title since the 2006 84 Lumber Classic.
Mathis matched Curtis with 67, dropping just a single shot Friday.
Cameron Tringale shot a bogey-free 65 to catapult himself into a tie for third, trailing Curtis by three shots heading into the weekend. Five birdies in the first six holes brought Tringale into contention.
First-round leader Matt Every came back to the field on Friday after his tee time was delayed by a weather system in San Antonio. After setting a course record Thursday, Every was 2 over in his second round and dropped into a tie for third. He completed 16 holes before play was suspended because of darkness.
The second round will resume at 7:30 a.m. Saturday.