Moss' effort was his ninth straight double-figure game dating to last season. J.R. Cadot scored 11 for the Horned Frogs (4-2), who shot 45.3 percent (29 of 64).
The Horned Frogs outrebounded Houston 36-31, led by Cadot's nine, and committed only 12 turnovers to the Cougars' 19.
Brown gave Houston its only lead on a 3-pointer with 9:11 left in the first half for a 21-20 edge.
TCU led 49-43 with 13:53 left before 7-0 spurt made it 56-43. The Horned Frogs coasted from there with a 43-32 second-half margin.