Reginald Johnson Jr. poured in 18 points and Brian Darden added 17 for Hampton (7-7, 3-0 Mid-Eastern Athletic), which shot 52 percent in the second half and held Bethune-Cookman scoreless over the final three minutes.
Hampton trailed by 10 early in the second half but steadily chipped away at the gap. Pressley's layup with 1:36 left tied the score at 70, then Johnson hit the go-ahead bucket and the Pirates padded it from the foul line over the final 21 seconds.
Ricky Johnson paced Bethune-Cookman (4-12, 1-1) with 20 points and Mario Moody added 15. Jordan Potts and LaRon Smith scored 12 apiece for the Wildcats, who were outrebounded 42-30 and have lost eight straight.