Peacock scored 15 of his points in the first half, while Lawal had 15 of his rebounds and all 12 of his points in the second half. Iman Shumpert had nine assists and nine points for the Yellow Jackets (8-4).
Tennessee State (3-9) scored eight straight to take a 39-37 lead 5 minutes into the second half, but the Yellow Jackets outscored the Tigers 17-5 to go ahead 54-44. Lewis Clinch hit a 3-pointer with 6:29 to cap the run.
Gerald Robinson Jr. led Tennessee State with 16 points and five assists and Darius Cox had 10 rebounds.
Georgia Tech trailed much of the first half before a 13-5 run late in the period put the Yellow Jackets ahead 33-26 at halftime.