Tre Roberson's 5-yard scoring run, and Coprich's 2-point conversion, gave the Redbirds the lead with 2:58 left.
Illinois State (7-1, 5-0) overcame three Matt Adam's touchdown strikes- all to Tonyan- in the second quarter, which put the Sycamores on top 21-9 at halftime.
Eric Heidorn's 38-yard field goal gave Indiana State (4-4, 2-3) a 24-9 lead.
But on the following drive, Coprich sprinted 44-yards to score to make it 24-16. Sean Slattery's 23-yard field goal early in the fourth cut it to 24-19.
Adam threw for 231 yards and Tonyan had 117 receiving. Roberson threw for 121 yards and rushed for 61 and two scores.