Brockman completed 35 of 46 passes for 321 yards as the Racers improved to 3-3. Duane Brady caught a 46-yard touchdown pass and also scored on an 8-yard run. Powell's TD catches were for 1 and 36 yards.
Donald Russell scored on runs of 4 and 9 yards for Georgia State, which lost its fourth straight after an opening win. The Panthers were 6-5 a year ago under veteran coach Bill Curry in their first season of football.
Brady caught seven passes for 91 yards and added 65 yards on eight carries. Murray State had 459 yards from scrimmage to 367 for Georgia State.
Georgia State's Drew Little completed 17 of 38 passes for 228 yards and was intercepted twice.