Ogbe made 9 of 15 shots from the field while Dillard scored 11 of his points from the free-throw line.
Morehead State (14-17, 8-8) broke open a 56-56 game with five straight points but Dillard answered with a jumper and two free throws.
From there, the teams exchanged the lead until Bakari Turner tied the game at 66 on a three-point play. But Jeremiah Samarrippas knocked down a trey on Tennessee Tech's next possession then two free throws at the 13 second mark as the Golden Eagles (12-17, 5-11) held Morehead State scoreless over the final minute to create the final margin.
Angelo Warner had 11 for Morehead State, which will take on Tennessee-Martin in the first round of the OVC tournament.