Armani Flannigan scored eight of his 10 points in the final 7 minutes, including four free throws down the stretch and a tip-in with 3:07 left that gave North Texas (3-0) all the points it would need at 57-51.
Delaware State (2-1) pulled within 47-46 on Tyshawn Bell's 3-pointer with 9:43 left, but North Texas answered with an 8-1 run.
After a 27-all tie at halftime, the Mean Green opened the second with a 10-5 run and never trailed from there.
DeAndre Haywood led the Hornets with 18 points. Bell added 16 and Kendall Gray 12. Both Haywood and Bell went 4 for 5 from 3-point range, but the rest of the Hornets were 0 for 13. Gray also had 13 rebounds.