The Aggies had a slim 25-20 lead with 4:40 left in the first half, then went on a 17-4 run to build an 18-point halftime lead, 42-24.
Houston pulled back to within eight, 59-51, with four minutes left in the game, but that was a close as the Cougars could get.
Guard Elston Turner led the Aggies with 26 points, while forwards Ray Turner and Kourtney Robertson each scored 14. .
The Aggies shot 49% from the field and had a 38-23 rebounding advantage, with Ray Turner pulling down 10 rebounds.
Texas A&M improves to 6-1 on the season and hosts Stephen F. Austin on Wednesday night.