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.
Shooting guard Jaylen Nowell, ranked No. 45 in the ESPN 100, chose the Washington Huskies on Wednesday over California. As a junior he led Garfield Heights to a state championship and was named MVP of the tournament.
Donnie Tyndall has filed an appeal to reverse the 10-year show cause penalty he received from the NCAA in April for violations that occurred while he was coaching Southern Mississippi.
Top-50 prospect Jaylen Nowell committed to Washington on Wednesday. Nowell, a shooting guard, is No. 45 on the ESPN 100.