Brent Arrington had 15 points and five steals for Morehead State (13-16, 8-6 Ohio Valley), while Billy Reader was 6 of 7 for 13 points.
Morehead State ran off a 16-3 stretch early, shot 59 percent in the first half - putting three players in double figures - and led 54-38 at the break.
The lead hit 20 less than two minutes into the second on Mashour's dunk. Tennessee State got as close as 10 points with five minutes left, but Angelo Warner drilled a 3-pointer and four consecutive free throws pushed the lead back to 17.
Xavier Richards led Tennessee State (5-24, 2-12) with 23 points. Jay Harris and Marcus Roper both added 12 points.