Billy Garrett Jr. added 16 points, Tommy Hamilton IV and Myke Henry 13 apiece for the Blue Demons, who had six players in double figures. DePaul was 31 of 57 for 54.4 percent, including 11 of 20 from the arc.
Fred Sims Jr. scored 22 points off the bench for the Cougars (3-6), who lost their fifth in a row. Jawad Adekoya added 17 points. Chicago State shot 35.2 percent and were only 8 of 29 from 3-point range.
Cain hit a 3-pointer and Hamilton two free throws to give DePaul a 14-point lead early in the second half. They led by double figures from there, going ahead by as many as 27.
It was the third straight win for the Blue Demons (4-3), who were playing their 500th game in the Allstate Arena.