Sullivan scored 22 points on 8-of-12 shooting while Felder added 19, shooting 6 of 11 and grabbing eight rebounds for the RedHawks.
Miami hit 57 percent of their shots from the field compared to Tennessee's 39 percent.
Miami (3-6), in recording its first road win of the season, was up 37-32 at the break, but came out shooting poorly in the first minutes of the second half. Tennessee State (1-11) failed to take advantage of the opportunity, losing grip on any comeback opportunity.
Patrick Miller, who leads the team in scoring with 20.5 ppg, scored 26 points but shot only 33 percent from the field for the Tigers who open conference play against Eastern Illinois next Saturday.