Roberson completed 12 of 16 passes for 222 yards and Lechein Neblett had four catches for 101 yards and two touchdowns.
Illinois State (3-0) racked up 27 first downs, punted just twice and scored a touchdown on its first five possessions of the second half. The sixth was an eight-play, 28-yard drive which bled the final 5:35 off the clock.
Austin Peay (0-4) has now lost 16-straight games dating back to a 38-31 win over Tennessee Tech on Nov. 17, 2012. The Governors didn't get a first down until the second quarter and had just 88 total yards in the first half as Illinois State jumped to a 20-0 halftime lead.
Austin Peay had nearly as many penalty yards (124) as total yards (174).