Rice (3-15, 0-5) wasn't much better from the field, making 35 percent of its field goals and 22 percent of its 3-pointers.
Rice held a 50-42 rebounding edge, led by Paulius Packevicius' 20 boards.
McKiver had five rebounds, while Smith finished with nine points, six assists and four rebounds. Kelvin Lewis added 10 points for Houston.
McKiver also led Houston with six steals, with DaShaun Williams adding four. The Cougars forced 29 turnovers while committing 16.
Four Owls scored in double figures, led by 16 from Packevicius. Patrick Britton and Rodney Foster scored 14 apiece and Lawrence Ghoram added 10.
- Send us your sports story tips
- Click here for more sports stories