Lawrence Cooks and Charles Wilson-Fisher added 16 points each for Hampton (5-10, 2-0 Mid-Eastern), which has won three straight. Cooks made a career-best five 3-pointers while Wilson-Fisher grabbed eight rebounds and had a career-high four blocks.
Savannah State (4-11, 1-1) trailed by as much as 14 in the second half but trimmed its deficit to 81-80 with Troyce Manassa’s 3-pointer, which capped a 10-3 run with 17 seconds left.
Hampton padded the advantage back to four down the stretch. Manassa and Casey Wells both missed shots at the other end in the closing seconds.
Dexter McClanahan scored 22 points and grabbed a career-best 12 rebounds to lead Savannah State. Wells finished with 17 points and Robert Kelly Jr. had 15.
The Tigers committed 17 turnovers.