Smith saw just 23 minutes of action from off the bench while scoring 10 points and grabbing six rebounds. He had only one turnover.
Louisville improved to 7-1, its lone loss having come last Sunday against North Carolina.
Montrezl Harrell led the Cardinals in scoring with 14 points. Chane Behanan had 11 points and 11 rebounds. Chris Jones and Luke Hancock joined Smith in scoring 10 points.
Missouri-Kansas City (1-6) was led by 14 points each from Nelson Kirksey and Martez Harrison.