Beane's 3-point play capped SIU's 9-0 run for a 37-29 lead late in the first half. Olaniyan scored the final five points of the half for an 11-point lead as Drake only made one field goal in the final five minutes.
Drake took its first lead of the second half at 61-59 on Reed Timmer's 3-pointer with nine minutes left. But Drake didn't hit another field goal until Timmer's at the 3:20 mark.
Southern Illinios made 4 of 6 free throws in the final 35 seconds to seal it.
Timmer finished with 27 points for Drake (5-13, 0-6), which lost its 10th game in the last 11.