Moore made 6 of 10 field goals, including 2 of 3 from 3-point range. Hooper Vint added 10 points for UTEP (2-0).
The Miners made 8 of 12 from behind the arc in the first half and took a 37-30 lead into the break.
Morris scored six points during an 11-0 run that gave UTEP a 55-41 lead with 12 minutes left. After a 3-pointer by Ethan Montalvo pulled Texas State (1-1) within five, Jake Flaggert made back-to-back 3s to cap a 10-3 spurt which pushed the Miners' lead into double digits for good.
UTEP made 14 of 23 second-half shots while the Bobcats shot just 30 percent after halftime.
Montalvo led Texas State with 16 points. Cameron Maylor added 15 and eight rebounds.