James Bennett's effort on 25 minutes was enough to send Hull through.
BARNSLEY: Letheren, Harban, Smith, Potter, Meynell, Butterfield (Loukes 54), McGrory (Beevor 45), Wroe, Jarman, Coulson (Fedorenko 82), McParland
Subs: Waggett, Frost
Booked - Jarman
HULL CITY: Duke, Matthews, Lamplough (Slater 56), Fry, Plummer (Belt 45), Frizzell, Russell, Bennett, Kendall, Wilkinson, Atkinson (Law 65)
Subs: Aspen, Devitt