Kaminsky capped his scoring with two free throws in the final 21 seconds that nailed down Wisconsin's (22-5, 9-5 Big Ten) fifth consecutive game.
Sam Decker padded the Wisconsin score sheet with 15 points and 11 rebounds. Josh Gasser scored 12.
Iowa (19-7, 8-5) had a double-double of 21 points and 11 assists from Roy Devyn Marble. Josh Oglesby scored 17.
The Badgers led 40-31 at halftime but the Hawkeyes grabbed a 64-60 lead on Marble's two free throws with 4:27 to play. Wisconsin took the lead back 71-70 with 1:20 to play when Bronson Koenig hit a jump shot off an assist from Traevon Jackson.