Tevyion Kirk scored 17 points with 9 of 11 free throws and Ohio (5-4) made 31 free throws to the Western Kentucky's 15 but was outscored 50-34 in the paint. James Gollon scored 13 points with three 3-pointers and Jason Carter added 12.
The Hilltoppers trailed by as many as 17 in the second half but rallied to within seven points on Marek Nelson's back-to-back 3-pointers with 1:58 to play. Taveion Hollingsworth's jumper made it a three-point game with 14 seconds to go, but Carter and Kirk each made a pair of free throws to seal it for Ohio.
Laster's go-ahead free throw put Ohio up for good, 7-6, and the Bobcats led 42-30 at halftime behind Gollon's 13 points.
Hollingsworth scored 19 points and Justin Johnson had 16 with 13 rebounds for Western Kentucky (6-3). Darius Thomspon, Dwight Coleby and Jake Ohmer scored 12 apiece.