Covington hit two 3-pointers, made four steals and sank nine of 10 free throws, including 4 of 4 in the final 25 seconds for the Tigers (3-5).
Three teammates also scored in double figures. Kellen Thornton finished with 17 points and Patrick Miller 14. Jordan Cyphers came off the Tennessee State bench to score 11 more.
For Alabama A&M (2-4), Brandon Ellis and Jeremy Crutcher scored 16 points apiece. Ellis was also a perfect 10 for 10 at the foul line, but his teammates only made 9 of 16 free throws. That was costly when Tennessee State went 27 of 34 at the foul line.
Demarquelle Tabb had a double-double for the Bulldogs with 15 points and 13 rebounds. Justan Banks scored 10.