Rhode Island (6-3), which has won five of its last seven games, dropped a close one to Providence 74-72 in its last outing.
Houston (5-1), playing away from home for the first time, trailed throughout most of the game. The Cougars were behind 33-21 at the half, and 51-39 with 6:35 remaining.
The Rams led 53-41 when Rob Gray Jr. scored 11 straight points and Houston closed to 57-52 with 2:50 remaining. Garrett made a layup and the Blackbirds hit eight free throws down the stretch to seal the win.
Damyean Dotson led Houston with 19 points and 12 rebounds.