Carlton Fay had 10 points for the Salukis (9-10, 4-4), who shot 53 percent from the field.
Isiah Martin, with 12 points, was the only player in double figures for the Sycamores (4-15, 2-6), who trailed throughout.
The Salukis led 27-24 at the break and went on an 11-3 run to take an 11-point lead early in the second half. They stretched their margin to 14 with 1:36 left.
Indiana State drew to within four early in the second half, but trailed by double digits most of the last 12 minutes.
The Sycamores shot just 29 percent overall, but outrebounded the Salukis 31-29.
Southern Illinois scored 24 points off turnovers.