The Bulldogs (8-11, 3-4 Missouri Valley) took command of the game early then held on in the closing minutes.
Osiris Eldridge scored 26 points, all in the second half, to lead the Redbirds (13-5, 4-3).
Drake, which never trailed, took a 16-6 lead on a 3-pointer by Templeton with 7:31 left in the first half and led by double digits the rest of the way. The Bulldogs were up 35-15 at halftime and then scored the first five points of the second half for their largest advantage, 40-15.
Illinois State put together runs of 10-1 and 9-3 in the second half but couldn't get any closer than 12 until the final minute.
Ryan Wedel added 14 points for Drake.