Johnny Hill had a career-high 24 points (all in the second half), Bryant Allen added 22 and Jackie Carmichael had 19 points and 12 rebounds for Illinois State (9-8, 0-5), which has lost five straight.
Drake trailed for most of the first half, falling behind 41-32 at halftime, but opened the second half with a 25-6 run to take a 57-47 lead with 12:43 remaining.
The Redbirds got as close as 77-73 on Hill's three-point play with 37 seconds left, but Drake hit 5 of 6 free throws the rest of the way to close it out.
SMU has signed a second player from Australia, 6-foot-11 forward Harry Froling, to a national letter of intent. The Mustangs previously signed guard Tom Wilson from Australia.
There's nothing to suggest the Jayhawks won't end up atop the Big 12 for a 13th season in a row. But what about a return to the Final Four?
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.