The Roadrunners (11-3, 1-0), who are off to their best start since 2001-02, shot 68 percent from the field in the second half (17 of 25).
After Diego Kapelan's 3-pointer tied the game at 60-60 with 3:54 left, Texas-San Antonio answered with seven straight points. Omar Johnson put the Roadrunners ahead 67-60 on two free throws with 1:46 to play.
The Cowboys (6-9, 0-1) led 32-28 at halftime, but missed three 3-pointers leading to six straight points by the Roadrunners. Gibson's jumper with 15:11 put Texas-San Antonio up 34-32, and they wouldn't trail the rest of the way.
Kapelan and Patrick Richard scored 15 each for the Cowboys, who lost their fourth straight.