Sullivan scored 13 of his points in the second half, leading the Redhawks back from a 10-points second-half deficit.
Washington hit two free throws with 5:23 remaining in the game for the Redhawks' first lead of the second half. His makes came during an 11-0 run for a 57-49 lead with 2:06 left.
Miami made 9 of 10 free throws in the final minute to seal it.
Antino Jackson scored 17 points for Akron (18-12, 9-8).
The Zips held a 23-17 lead at halftime after Miami went without a field goal for the final 7:47 of the half.