Coming off the bench, Thornton scored a team-high 20 points on 7-of-19 shooting and added 10 boards and a career-high five steals.
Covington made 8-of-15 attempts for 19 points and secured a game-high 13 rebounds.
Patrick Miller followed with 18 points, six boards and four assists. His four dishes make him TSU's single-season leader with 195.
TSU, which came into the game shooting 44.6 percent from beyond the arc in its last six contests, made just 7-of-32 attempts for a 21.9 clip.
The teams seemed to be feeling each other out to start the game as neither side could gain an advantage through the game's first six minutes. The Tigers and Aces were both 4-of-11 from the floor to start the game and the score was tied at nine apiece.
From that point, Evansville went on an 11-4 run to take a seven-point lead with just under 11 minutes to play in the first half. Five different Aces had points during the stretch and EU made five of its seven attempts.
The Tigers clawed back to within one, 21-22, when Miller and Jay Harris canned back-to-back triples. Harris's jumper was set up by a heads-up steal from Covington on the other end of the court.
Another big run by the Purple Aces, this one 10-0, put them in the driver's seat, 34-23, with 4:39 left in the opening frame. TSU was 0-of-3 during the cold spell and had a pair of turnovers.
Miller ended the first-half scoring with a layup, but TSU still went into the break trailing, 29-38.
TSU never led in the first period.
Tennessee State made 11-of-35 shots (31.4 percent) during the game's first 20 minutes and was outscored in the painted area 26-14.
Evansville extended its lead to 14 during the first five minutes of the second stanza after scoring seven straight points. TSU again helped the Purples Aces' cause with four fumbles and a 0-for-4 line from the floor during the run.
TSU tried hard to mount a comeback and Covington capped an 8-0 Tiger run with a layup at the 8:13 mark. Unfortunately for TSU, his basket only put Tennessee State within 12 at 64-52 and Evansville countered with an old-fashioned three-point play on its next possession.
The Tigers chipped away at the lead and got within eight when Thornton hit a triple with 1:54 to go, but Evansville made 8-of-8 free throws down the stretch to hold on for the 84-72 victory.
TSU outrebounded EU 40-39, but had 17 turnovers compared to just 15 for the Aces.