The Sycamores (6-3) also got 16 points from Jake Odum, 12 apiece from Justin Gant and R.J. Mahurin and 10 from Dawon Cummings to advance to Sunday's semifinal round, where they will play the winner of San Francisco and No. 18 San Diego State.
Jarvis Summers made two free throws 15 seconds into overtime to give Ole Miss its first lead since it led 27-25 with about 8 minutes left in the first half.
Marshall Henderson led Ole Miss (8-2) with 27 points. Reginald Buckner scored 17 points with 10 rebounds and Murphy Holloway added 16 points and 13 rebounds.
Indiana State held a 44-33 lead at halftime and it was 75-all heading to overtime.