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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.