Smith scored 17 of his points after halftime.
Chane Behanan fired in 20 points and Peyton Siva added 19 for the Cardinals (12-1), who reeled off their seventh straight win.
The Wildcats (8-4) fell to their intrastate rivals for the first time in five meetings despite Archie Goodwin's 22 points. He committed five turnovers, however.
Ryan Harrow also reached double figures with 17 points for Kentucky.