Sean O'Brien added 12 points and Bola Olaniyan scored 11 for Southern Illinois.
Beane hit three 3-pointers and scored 11 points during a 20-6 run that gave the Salukis (19-7, 8-5 Missouri Valley Conference) their biggest lead of the game, 34-21, with 6:41 left in the first half.
SIU led 42-35 at the break and a 6-0 spurt pushed its lead to 56-45 with 13:28 to play, but Niels Bunschoten scored 11 during a 15-4 Indiana State (13-12, 7-6) run that tied it, 60-all, about five minutes later.
Smithpeters hit a pair of 3s during a 12-3 surge that made it 78-69 with 3:17 remaining and Southern Illinois held on from there.
Bunschoten led the Sycamores with a career-high 21 points.
