Delaware (9-12, 3-6 Colonial Athletic Association), which won for only the second time in its last seven games, overcame a 10-point deficit late in the first half.
The Panthers (5-15, 3-6), who have lost six of their last seven games, had their lowest point total of the season.
Trailing 27-20 at halftime, the Blue Hens scored the first 13 points of the second half to take their first lead of the game. Back-to-back 3-pointers by Carter gave Delaware a 33-27 advantage with 15:52 remaining and completed a 16-0 run.
Georgia State went scoreless for 5:36.
Brian Johnson added 10 points and eight assists for the Blue Hens.
Dante Curry led Georgia State with 15 points.