While Millwall boss Alex Neil opted to field the same XI from the first leg on Friday, Jakirovic made two changes, opting to drop his two eventual match-winners, bringing in Joseph and Semi Ajayi and playing with a back three.
The visitors made a bright start and looked dangerous from set pieces, with Charlie Hughes drawing a save from Patterson and then heading wide.
Millwall, who have been outside the top flight since 1990, then began to take control of the game on their home turf, with Femi Azeez forcing a save from Ivor Pandur with a shot from a tight angle after a sustained period of pressure.
The pivotal moment came late in the first half when Joseph’s foot appeared to get caught under a challenge from Thierno Ballo, forcing him off injured.
To the astonishment of his manager, Algerian Belloumi was not ready to come on, which meant his side had to play briefly with 10 players.
However, once the second half kicked off, the 23-year-old’s impact on the right wing was clear and it was he who came up with the game’s biggest moment of quality.
Moments after Barry Bannan and Alfie Doughty had come on for Millwall, Belloumi found himself one-on-one with Doughty on the right, took a step inside and stunned The Den with a goal worthy of winning any game.
Belloumi was also at the heart of Hull’s second goal, stealing the ball from Milllwall captain Jake Cooper on the halfway line and surging upfield, before switching the play across to Gelhardt on the other side.
Gelhardt took a touch before firing low across goal and his former Sunderland team-mate Patterson got both hands to it but could not keep it out, with possibly the deftest of deflections off Ryan Leonard making an impact.
As Millwall threw players forward, spaces opened up and Matt Crooks had a chance to put the game out of sight, running clean through but chipping the ball into the hands of Patterson.
