Jared Berggren added 16 points and 14 rebounds for the Badgers (16-7, 7-3 Big Ten), who snapped a three-game losing streak to the Hawkeyes.
Mike Gesell led Iowa (14-9, 3-7) with 14 points and Aaron White added 13.
Wisconsin, which has shot less than 62 percent from the foul line this season, converted 13 of 14 free throws in the two overtime periods.
With Wisconsin leading 72-68 in the closing seconds, Berggren stepped out of bounds on the inbounds play, giving the ball back to the Hawkeyes. White scored and was fouled, but he missed the free throw.
Ryan Evans, who shoots 40 percent from the line, grabbed the rebound, was fouled and converted both attempts to seal the win.