The Panthers (7-3) took a 38-29 lead at the half and held the Golden Eagles (5-5) to 26 percent shooting (7 of 27) in the second half while forcing 22 turnovers.
Chip Armelin had 16 points and Rasham Suarez 12 for Southern Miss, which went 12 of 30 from 3-point range and 7 of 19 inside the arc. Armelin and Suarez both had four treys.
Harrow had four 3-pointers in the first 11:26 to give the Panthers a 20-15 lead and his fifth trey made it 32-18 at the 5:53 mark.
Armelin scored five points during the Golden Eagles' 9-0 run spanning halftime to get within 38-33 but Georgia State answered with a 15-2 run.