Southern Illinois scored the final four points of the first half and the first nine points of the second to go ahead 34-16. Indiana State never mounted a challenge from there as the Salukis extended their lead to as much as 23.
Desmar Jackson had 16 points, Olaniyan scored 12 and O'Brien added 11 for SIU (7-15, 3-6 Missouri Valley). O'Brien and Olaniyan each had 12 rebounds.
Southern Illinois made up for 2-of-12 3-point shooting by shooting 52 percent overall and 25 of 38 on free throws. Indiana State was only 11 of 22 at the free-throw line.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.
Wisconsin forward Nigel Hayes has withdrawn from the NBA draft and will return to the Badgers for his senior season.