Palmer was 9 of 12 from the field for the Cougars and hit all four of his free throws. He also had four blocked shots and four steals. Jawad Adekoya and Anthony Eaves scored 15 points each, Kieran Woods added 14 points and Fred Sims, Jr. had 13.
The Cougars finished with a 50-35 rebounding edge and hit 47.7 percent from the field and 85.7 percent from the free-throw line.
Chicago State had a 44-29 advantage at the break and cruised to the win.
Quentin Palmer led the RedHawks with 23 points on 6-of-12 shooting from the field. He sank 3 of 4 from distance and had five rebounds.