Chris Fouch had 15 points to lead the Dragons (16-5, 8-2), who broke free from a tie game by scoring 18 of the final 27 points before the intermission and then the first eight points of the second half to take a commanding 46-28 lead with 15 minutes, 16 seconds left.
The 8-0 run to start the second half capped a backbreaking 27-9 stretch over 11:10 that lifted the Dragons to their 14th victory in their last 15 games.
Frantz Massenat added 13 points, and Samme Givens had 12 points and 10 rebounds for Drexel.
It was a matchup between the top two defensive teams in the conference. Drexel entered holding opponents to a CAA-best 54.8 points, while the Panthers (14-7, 6-4) limited opponents to 58.2. Both are among the leaders nationally, with Drexel beginning the week sixth in the country and Georgia State 16th.
Drexel held an opponent to 60 points or fewer for the 10th consecutive game while keeping an opponent to 50 points or fewer for the eighth time this season.
The Dragons hadn't lost since a 58-44 loss at Georgia State on Jan. 2. The Panthers also entered playing well, having won 14 of 17.
Damion Lee, who averages a team-best 12.3 points but has scored 16.0 points while netting double figures in each of the last five games, picked up his third foul with 9:23 left in the first half. He finished with five points, but it didn't matter for the Dragons.
Givens led a balanced attack with eight first-half points for Drexel, which trailed by as many as six in the first half, to lead 37-28 at halftime.