The Salukis (7-4), who improved to 4-0 at home, shot 49 percent from the field. Jordan Caroline, Jalen Pendleton and Bola Olaniyan each scored eight points. Pendleton dished out five assists and grabbed three steals.
Marcus Roper paced Tennessee State (2-8), hitting six 3-pointers to total 23 points on 8-of-15 shooting overall. Jay Harris had 13 points with seven assists and Demontez Loman chipped in six points with 13 rebounds and four blocks.
Beane converted a three-point play and hit a 3-pointer to ignite a 17-0 run early in the second half that pushed Southern Illinois' lead to 49-30 at the 11:29 mark.
The Tigers trailed by double digits the rest of the way until a trio of 3-pointers made it 63-55 with 2:09 left.