Shon Abaev scored 10 points and the Bearcats (6-2) got 14 points from the bench and shot 42% (15 of 36) from 3.
Ocypher Owens led the Texans (5-4) with 16 points, Kaia Isaac scored 13 and Freddy Hicks 12.
Owens' layup with 11:49 left brought the Texans within 52-45 and capped a 14-7 Tarleton State spurt that lasted a little more than five minutes.
Cincinnati countered when Miller made two foul shots, Thomas went on a personal 8-4 run with consecutive 3s and a layup and Miller had a dunk with 8:12 left for a 64-49 lead. The Bearcats stayed ahead by double figures the rest of the way.
The Bearcats appeared ready to blow it open early when Thomas made a 3 for a 24-12 lead with 8:13 before halftime. But Tarleton State responded and outscored Cincinnati 17-7 to get within 31-29 at halftime.
Up Next
Tarleton State hosts Division III Howard Payne on Wednesday.
Cincinnati will make the 2 1/2-mile trek to face nearby Xavier on Friday.
___
Get poll alerts and updates on the AP Top 25 throughout the season. Sign up here and here (AP News mobile app). AP college basketball: https://apnews.com/hub/ap-top-25-college-basketball-poll and https://apnews.com/hub/college-basketball