Harrison was 9 of 16 from the field, and has scored at least 20 points in each game for Tulsa (4-0). James Woodard added 16 points with 10 rebounds.
Devonte Brown and Khristian Smith scored 14 points apiece to lead Indiana State (2-2).
The Sycamores led 40-31 with 17 minutes left. Woodard made a 3-pointer to spark a 16-5 run and give the Golden Hurricane a 47-45 lead with 12 minutes left, their first since the 13-minute mark in the first half.
Marquel Curtis made a 3-pointer to stretch Tulsa's lead to 58-54. Brown made a layup and Niels Bunschoten a pair of free throws to tie at 58 with 2:38 left. D'Andre Wright scored four points as part of a Tulsa 9-1 surge to seal it.