Norfolk State trailed 32-24 at the break, but took the lead at 36-35 on a 3-pointer by Kievyn Lila-St. Rose. The Spartans started the second half on a 20-5 spurt.
Marcel Boyd's three-point play ended Howard's dry spell and pulled them within 44-40 with just over 10 minutes remaining. But Maye's 3-pointer made it an 11-point game with 5:29 left.
Anell Alexis added 13, nine from the free throw line, for Norfolk State (16-11, 10-3 Mid-Eastern Athletic Conference).
James Daniel scored 20 points for Howard (6-22, 4-9), while Prince Okoroh had 13 and James Miller 10.
Daniel scored six consecutive points for Howard, including back-to-back 3-pointers, willing his team back within 62-60. But the Bison would not score in the final 2 minutes.