The victory has given Flitcroft's side a good chance of staying in the Championship ahead of the final game of the season next week.
"[It was] a special day. Focus was on Hull but we had a full week to prepare and the players did everything expected of them and more," the Barnsley manager told reporters after the game.
Flitcroft reserved special praise for Kelvin Etuhu, who performed impressively on his return to the side.
The 39-year-old added: "Etuhu was monumental - I had cramp just watching him!"
Barnsley travel to Huddersfield Town on the final day of the season.