Simmons' winning score came with just over a minute left in the game, breaking a 10-10 tie.
The Bulldogs (3-2, 1-0 Mid-Eastern Athletic Conference) trailed 3-0 until late in the third quarter when Tyler Scandrett hit a 35-yard field goal. Early in the fourth, Adrian Kollock, Jr. took it in from a yard out to give South Carolina State a 10-3 lead.
Hampton's Jorrian Washington ran 57 yards for a touchdown to tie the game again with 10 minutes remaining.
Following Simmons' tie-breaking score, Marquise Jones sealed Hampton's fate by intercepting Jaylian Williamson with under a minute to play.
Williamson was 19 of 32 for 182 yards for the Pirates (1-4, 0-1) and threw two interceptions. Washington ran for 176 yards on 18 carries.