Oberlin pulled within one point three times in the second half, the last when Nathan Cohen hit a 3-pointer to make it 42-41 with 12:18 remaining. Hain scored the next six points, sparking a 23-5 run to stretch Youngstown State's (1-1) lead to 65-46 with 4:45 to play.
Sidney Umude's free throw gave the Penguins their largest lead, 70-48 with 2:25 left.
Shawn Amiker had 13 points and nine rebounds. Marcus Keene scored 12 points, and DJ Cole and Fletcher Larson each added 10 for the Penguins, who shot 39.7 percent from the floor.
Cohen finished with 15 points on 4-of-11 shooting and dished out five assists. Matt Walker added 10 points for Oberlin.