No. 2-seed Houston has won eight straight and faces 10th-seeded Rutgers in the Midwest Region's second round on Sunday. It's unclear if starting guard DeJon Jarreau will be available after he missed all but 41 seconds with what appeared to be a right hip injury.
Tramon Mark added 15 points in place of Jarreau and Marcus Sasser finished with 14 for Houston (25-3).
D'Moi Hodge scored 11 points and Torrey Patton had eight points and eight rebounds for the Vikings (19-9). Cleveland State had won at least one game in each of its two previous tourney appearances, beating Indiana (1986) and Wake Forest (2009).
Hanging with Houston, No. 6 in the AP poll, was simply too much to ask - even on a neutral court that had at least a measure of tournament atmosphere. Fans gathered early in the concourse, took photos of statues, lined up for concessions and some brought signs.
The vocal crowd provided energy throughout the game, too, even as Houston struggled to pull away early.
Grimes' basket to end the first half gave the Cougars a 37-29 lead and they opened the second half on a 12-2 run, holding the Vikings to just one basket over the first five minutes.
Cleveland State was 5 of 19 from the field in the second half.
Houston is in its third straight tourney - its longest streak since 1982-84, when the team dubbed Phi Slama Jama lost in back-to-back title games.
Houston in March Madness: UH beats Cleveland State 87-56
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