Norfolk State trailed 39-29 at halftime but outscored NC A&T 46-29 in the second half - including an 11-1 run to open the half to tie it at 40-all.
Norfolk State led by eight points with 1:27 left, but two free throws by Sam Hunt, a steal and a Hunt layup made it 67-63. After two Norfolk State free throws, Hunt hit a 3-pointer with 28 seconds left to cut it to 71-68.
Oliver made it a two-possession game with a layup at the 24-second mark and added another in the closing seconds.
D'Shon Taylor and Preston Bungei had 13 points apiece for Norfolk State (8-12, 4-1 Mid-Eastern Athletic Conference).
Hunt led NC A&T (5-15, 2-4) with a career high 34 points - 24 coming in the first half.