Darrion Pellum added 18 points for the Pirates (23-8), who will face two-time defending tournament champion Morgan State (17-13) on Saturday.
Hampton trailed 24-14 in the opening half but came back to take a 37-33 halftime lead. The Pirates continued to lead, 44-39, with less than 15 minutes to play and used a 20-5 run, capped by two free throws from Morgan, to pull ahead 64-44 with just over 6 minutes left.
The Spartans (12-20) went 9:30 without a field goal in the second half, turning a seven-point hole into a 22-point deficit with 4:10 remaining
Kyle O'Quinn scored 19 points and grabbed 17 rebounds for Norfolk State. Rob Hampton added 15 points, Brandon Wheeless had 11 and Tim Zephyr 10.