Coprich had scoring runs of 11, 22 and 75 yards - for the 10th Illinois State touchdown of 50-plus yards. He was four yards away from tying a career-high set against Eastern Washington.
Southern Illinois led 21-14 at halftime after Mark Iannotti's three touchdown passes. But Tre Roberson had rushing touchdowns of 13 and 23 yards on back-to-back drives - sandwiched around a Southern Illinois fumble - early in the third quarter.
Roberson was 4-of-13 passing for 88 yards and had 13 carries for 72 yards with two scores for Illinois State (8-2, 6-1 Missouri Valley). Five runners combined for 372 yards rushing and six touchdowns.
Iannotti threw for 329 yards on 42-of-62 passing with one interception for Southern Illinois (3-7, 2-5).