Sheehey hit 13-of-20 shots from the field for the Hoosiers (16-12, 6-9 Big Ten) while the other four Indiana starters combined for a modest 21 points.
Stanford Robinson scored 17 for Indiana off the bench. Fellow reserve Evan Gordon contributed 12 points.
Roy Devyn Marble led Iowa (19-9, 8-7) with 20 points. Aaron White added 19 points and 10 rebounds. The Hawkeyes lost their third in a row.
Iowa led 52-49 at halftime, but hit a dreadful cold spell in which they scored two baskets in a stretch of roughly five minutes.