Hampton (15-11, 10-3 Mid-Eastern Athletic Conference) opened up a 73-60 lead with 4:27 remaining when Maxwell finished a fast break with a dunk. Howard responded with an 18-6 run, including 11 points from James Daniel, to pull within one.
Daniel had a chance to tie the game, but missed the first of three free throws with 6 seconds to play.
The two teams combined for 64 fouls and 92 free throw attempts.
Daniel scored a career-high 38 points, knocking down six 3s and 16 of 24 free throws, but finished with nine of Howard's (6-21, 4-8) 20 turnovers. Tyler Stone added with 17 points.