Robert McKiver led the Cougars (11-2), who had their 10-game winning streak snapped, with 15 points, while Tafari Toney had 14, and Dion Dowell and Lanny Smith added 12 each.
Dowell hit a 3-pointer with a 1:11 left to tie the game at 89-89, but UMass hit six free throws to pull away.
Houston shot 53 percent and limited UMass to 40 percent from the field in the first half to pull ahead 48-37 at halftime. With the score tied at 8-8, a basket by Smith and a 3-pointer by Toney put the Cougars in charge.
The shooting percentages were reversed in the second half with UMass shooting 53 percent and Houston hitting 38 percent of its shots.
The Minutemen took their first lead of the second half, 71-70, on Lowe's layup with 8:40 to play.
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