The Cougars, without senior point guard and star player Jamal Shead, who left the game with a severe ankle sprain in the first half, stuck around in the second half and had a chance.
After Emanuel Sharp brought UH to within three in the final minute with an and-one layup, Houston had one final shot to tie the game with 8.9 seconds remaining.
Sharp caught the inbounds pass, stepped back for a three, and missed it off front-iron.
And the season was over. UH fell in the Sweet 16 for the second straight year after falling to the Duke Blue Devils 54-51 Friday night.