Harrow, who missed the game with concussion-like symptoms, ranks 10th in Division I averaging 20.4 points per game. Georgia State is 4-0 this season without him.
Markus Crider added 10 points, eight rebounds and four assists for the Panthers (17-8, 10-4 Sun Belt), who have won six of seven and posted the program's third-best record through 25 games.
Texas State (11-13, 5-10) finished with just 12 total field goals (29.3 percent), the fourth straight opponent Georgia State has held below 30 percent shooting.
The Panthers opened on a 14-5 run and never trailed in the game, extending their lead to as many as 15 in the second half.
Emani Gant had 13 points to lead the Bobcats.