Northern Kentucky (6-8) jumped out to an early six-point lead on back-to-back 3-pointers by Tyler White and Deontae Cole, but Youngstown State chipped away and was down by just one at the break, 41-40.
The Penguins (9-6) opened the second half on a 16-6 run - six by Shawn Amiker - and led by as many as nine before the Norse rallied to trail by three with 2:15 left.
Hain's jumper with 1:48 put the lead back to five and Northern Kentucky wasn't able to answer.
Marcus Keene had 11 points for the Penguins. Osandai Vaughn and Amiker both finished with 10 points.
Chad Jackson paced Northern Kentucky with 16 points. Tayler Persons added 15 while Jalen Billups, White and Cole all finished with 12 points apiece.