Butler took advantage of being in the double bonus and converted all six free-throw attempts in the final 24.5.
Tre Demps and Bryant McIntosh scored 18 points apiece for the Wildcats, who have lost seven straight.
The Hoosiers lost their previous two games by double digits and were playing for the fourth time in nine days.
Watch The Zone from Friday, January 30 on WISH-TV.
Carmel defeats Ben Davis 50-41.
North Central defeats Warren Central 81-67.
Zionsville defeats Brownsburg 68-59.
Lawrence North defeats Center Grove 69-63.
Bloomington South defeats Terre Haute South 70-52.
Franklin Central defeats Bloomington North 57-55 in 2OT.
Perry Meridian defeats Terre Haute North 61-52.
Hamilton Southeastern defeats Noblesville 51-49.
Avon defeats Westfield 70-55.
Brebeuf defeats Chatard 51-38.