Damion Lee scored 18 points to lead Drexel (2-6), which dropped its second in a row and fourth in five games. Kellen Thornton tallied 20 points to pace the Tigers (4-5).
Tennessee State shot 50 percent from the field compared to 39 percent for the Dragons.
Drexel erased a 36-30 halftime deficit to lead for much of the second half, although its advantage was never more than three. Its last lead came at 57-55 on a Frantz Massenat (15 points) layup with 4:49 to play.
The Dragons, who have lost four games after leading at halftime, were unable to capitalize on a 40-30 rebounding edge, including a 19-8 advantage on the offensive boards.
"We've been losing the same way all season," Flint said. "We're eight games in now. You got to feel we've got to do some things differently. We just haven't been doing them."
Tennessee State seized control once Thornton went to his pump fake on the block to tie it at 57. Drexel had a shot blocked on the other end and couldn't retreat on defense to stop a Jordan Cyphers' layup that put the Tigers in front to stay.
Cyphers (15 points) missed a foul shot that would have completed a three-point play, but Michael Green grabbed a rare Tennessee State offensive rebound and cashed it in for a 61-57 lead. When a wide-open Cyphers hit a three-pointer from the right corner with 2:51 left to cap a 9-0 spurt, the Dragons were done.
"All of our games have been relatively close the last five or six minutes, and we just haven't been able to come up with stops," Lee said. "The scoring isn't . . . that's not one of our problems. It's digging down and getting a stop when we need it.
"I think it's mental lapses as a unit. As a unit, we start to take breaks. And as Coach always says, we play not to lose. We play just to run time out and to win by as little as possible. That hasn't happened. And we give teams confidence throughout the game. I don't know what to tell you."