The Raiders (17-9, 10-4 Horizon League) trailed 68-67 with 1:18 left to play when Cole Darling knocked down two free throws to give Wright State a 69-68 lead.
N'Gai Evans, who finished with 17 points, added a layup and a pair of free throws in the final 1:01 to seal the win. Cole Darling scored 11 points and Matt Vest added 10 for the Raiders, who scored 23 points off 15 turnovers.
Vytas Sulskis led the Penguins (8-16, 2-12) with 26 points, matching a career high. Sulskis was perfect in the first half, scoring 20 points on 7-of-7 shooting, including four 3-pointers and a pair of free throws.
Kendrick Perry added 16 points for Youngstown State, which has lost seven of its last eight games.
The teams were tied 15 times and exchanged leads on 16 occasions.