The Salukis (18-3, 6-1 Missouri Valley) have won four straight, 10 of 11 and are an NCAA-leading 8-0 on the road.
Olaniyan was 7-of-9 shooting. Tyler Smithpeters was perfect on four 3-point attempts and scored 13 points. Mike Rodriguez also scored 13 points with Lee Vincent adding 11 and Sean O'Brien 10. Anthony Beane had a career-high six assists.
Dequon Miller scored 22 points for the Bears (8-12, 4-4), who had won three straight MVC games for the first time since 2010-11. Ryan Kreklow added 14 points and Jarred Dixon 10.
Southern Illinois led from early on, building a permanent double-digit lead with nine minutes left in the first half. The Salukis took their biggest lead of 23 points, 62-39, with 10:34 left in the game after four points from Olaniyan.