After falling behind 10-0 in the first quarter, Carter threw an 11-yard touchdown pass to Da'Kendall James to cap a 12-play, 78-yard drive. Kevin Johnson put the Spartans up 13-10 with 14-yard run and it was 16-10 at the half.
Just three minutes into the second half, Price had his pick-6 for a 23-10 lead.
Norfolk State (5-6, 4-3 Mideastern Athletic Conference) won its third straight, its longest streak since 2011, the last time it won five games in a season.
Delaware State (2-9, 1-7) had 303 yards of total offense, just 10 less than Norfolk, but had three turnovers.