Tyler Laser scored 13 points, including the 3-pointer that put the Panthers (3-4) ahead for good at 62-61 with 4:31 left. Jeremy Granger added 12 points, and Curry McKinney grabbed a game-high 10 rebounds.
Tennessee State shot 50 percent (22 of 44) to Eastern Illinois' 45.7 (28 of 61).
Covington put Tennessee State ahead 61-59 with 5:03 left before Laser's 3-pointer and two free throws by Hollowell gave Eastern Illinois a permanent lead.
The Panthers broke a school record with their seventh consecutive league victory, dating back to last season.