Adam Johnson had given the hosts the perfect start on Boxing Day, scoring in the opening 30 seconds, but goals from Gaston Ramirez on the half hour mark, James Chester five minutes into the second half and Nikica Jelavic at the death saw the Tigers take all three points.
Johnson carried on from where he had left off, following Sunday’s last-minute Tyne-Wear derby winner, pouncing on Curtis Davies’ weak back pass, jostling with the centre-back for possession and then rounding Allan McGregor to give the hosts the lead inside a minute.
Johnson featured heavily in an opening period in which Sunderland might have increased their lead with 16 minutes gone, had Liam Rosenior not managed to get a block on Sebastian Larsson’s goal-bound shot.
The Black Cats enjoyed the majority of possession and dominated the opening period of the game but were pegged back when Ramirez’s shot from 20 yards skipped over a horrified Costel Pantilimon in the Sunderland goal.
Poyet’s men came close to restoring their advantage during a flurry of activity at the end of the half with Alex Bruce and Stephen Quinn fortunate to survive appeals for handball in the area before Sebastian Larsson had a header cleared off the line.
McGregor then beat away a near-post shot from defender Santiago Vergini in stoppage time to ensure the sides entered the break level.
Sunderland were unable to start the second half as they had the first and it was Hull who would take an early lead. With the Black Cats untidy during the opening minutes of the second half, Robbie Brady tested Pantilimon with a 50th-minute free-kick which was turned away for a corner.
Ramirez delivered the resulting set-piece to the near post and Chester got in front of Vergini to power a header into the top corner.
Sone Aluko spurned a great chance when he shot tamely into Pantilimon’s hands and it was left to substitute Jelavic to seal the win.
With the hosts pushing for an equaliser in the closing stages, the Tigers broke through Ahmed Elmohamdy who fed the ball into the path of the Croatian who guided a low shot under the keeper to hand Hull their league first win since October and move them out of the bottom three.
Sunderland: Pantilimon (6), Vergini (5), Coates (6), O’Shea (6), Jones (5), Cattermole (6), Alvarez (5), Larsson (6), Gomez (5), Johnson (7), Fletcher (7).
Used subs: Altidore (4), Giaccherini (5), Buckley (5).
Hull City: McGregor (7), Chester (6), Bruce (5), Davies (5), Rosenior (6), Elmohamady (7), Meyler (5), Quinn (5), Brady (5), Ramirez (7), Aluko (6).
Used subs: Jelavic (6), Sagbo (4), Ince (4).
Man of the Match: Gaston Ramirez