The Sycamores (12-3, 3-0 Missouri Valley Conference) closed the first half on a 20-8 run sparked by 3-pointers from Dawon Cummings and Odum to lead 40-30 at halftime.
Drake (10-5, 1-2) crawled back to take a 54-50 lead at the midway mark in the second half.
With the score tied at 59, Arop hit a 3-pointer to grab the lead and ignite a 9-3 run. Cummings added another from beyond the arc with 57 seconds remaining to make it 71-63. Indiana State made its last six free throws to seal the win.
The Sycamores made nine 3-pointers and went 16 of 18 from the free-throw line. Cummings had 13 points and Khristian Smith contributed 12.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.