Goode finished with 11 points and 11 rebounds for the Spartans (10-10, 5-0 Mid-Eastern Athletic Conference), who have won four straight games. Rob Johnson scored 11 points and Pendarvis Williams added 10.
Norfolk State trailed 30-29 when Coppin State's Zachary Burnham scored on a layup with 15:41 left to play. But the Spartans regained the lead, pulling ahead by as many as 16 points.
Coppin State cut the deficit to five points with 34 seconds left, but did not pull closer the rest of the way.
Andre Armstrong scored 22 points for the Eagles (4-15, 1-3), who have lost six of their last seven games. Michael Murray finished with 17 points and nine rebounds, and Taariq Cephas had 14 points and six assists with eight turnovers.