Hampton now has won seven of the last nine meetings between the teams and is 28-13 all-time against the Hornets.
Jaylian Williamson found Shakim Alonzo with a 21-yard pass for the game's first score less than five minutes into the game, but Delaware State (0-5, 0-2 Mid-Eastern Athletic Conference) answered with Mike Waters' 2-yard run for a score barely three minutes later.
Prevost kicked a 35-yard field goal as time expired in the first half to give Hampton (2-3, 2-1) the lead for good, 17-14, and added an insurance field goal in the third period from 32-yards out.
Hampton limited the Hornets' rushing game to just 53 yards on 32 carries.
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The Cyclones are for real, with a rising star in coach Matt Campbell and a QB who turned down Alabama.
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Fifty years ago, Nick Saban won his first title, at West Virginia's Monongah High. His teammates remember a determined, cerebral leader who always thought three steps ahead. Sound familiar?
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Kiper: This year's draft is 'all defense'
Mel Kiper on why he only has three offensive skill players on his big board and if anyone can challenge Nick Bosa for the top pick.