Indiana State will play No. 20 Loyola Chicago in the semifinals on Saturday.
Evansville scored 14 second-half points, a season low for the team.
Evan Kuhlman and Noah Frederking each had 10 points for the Purple Aces (9-16). Shamar Givance scored eight points and had seven rebounds. Jawaun Newton, whose 13 points per game coming into the contest ranked second on the Purple Aces, had six points on 2-of-11 shooting.
Indiana State led 31-29 at the half, and neither team built a large lead until the Sycamores began to pull away in the final minute.