There was tumult on and off the pitch at the Den but after Neil Harris’s redoubtable Lions claimed their third Premier League scalp one thing is certain: League One Millwall will join non-league Lincoln City in the quarter-finals of the FA Cup.

A post-match pitch invasion in which missiles and punches were thrown added a sour note to this fifth-round tie and required police horses to disperse it. But that should not detract from another unstinting Millwall performance and they will now be happy to take on all-comers, especially at home. As for Leicester, who join Bournemouth and Watford in finding their nemesis at the Den, last season’s miracle continues its transformation into nightmare.

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Shaun Cummings’ wonderful winner, scored in the 90th minute, came after Millwall had been reduced to 10 men –Jake Cooper was given a second yellow card on the hour mark. Instead of confounding the home side, the sending off galvanised them and provided a platform for victory even Claudio Ranieri had to admit was deserved.

The upset had been predicted by many, such has been Leicester’s woeful league form, while Millwall had not lost since mid-December and not conceded a goal in eight hours. But the first half had a conventional feel to it. A scratch Leicester side, with Ranieri making 10 changes from the defeat to Swansea, was surprisingly cohesive and looked like it had enough ability to cause Millwall harm.

Key to Leicester’s first-half performance was Shinji Okazaki. The Japan striker has been mystifyingly absent for much of the Foxes’s league season but looked a cut above the rest of the players in the opening 45 minutes. In the 16th minute he span past his marker, Byron Webster, to bear down on Jordan Archer in the Millwall goal. Webster got back at him and Okazaki stumbled, but still managed to lay off the ball to the winger Demarai Gray, whose left-foot shot was blocked.

A minute later, from a corner, Okazaki found a powerful header that forced Archer into a reaction save. Ten minutes after that he had another chance to give Leicester the lead, but failed to anticipate an early cross from Bartosz Kapustka.

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Millwall were not quite themselves. As it became clear Leicester were ready to play, the home side seemed to lose a little confidence and suddenly the ravenous energy was not as apparent. Their best moments in the first half came from set pieces and the scraps that followed. One melee after a fumble by Ron-Robert Zieler earned Cooper his first yellow card. But in truth the German goalkeeper was not properly tested.

The second half began with Leicester continuing to look the hungrier and within 10 minutes they had a significant advantage. A break saw Kapustka thread the ball to Ahmed Musa on the right. He had Cooper in close attention and spun him to invite the challenge. It duly arrived, Musa went over it and the referee, Craig Pawson, opted for a second yellow card.

A few minutes later, Okazaki was inches away from meeting a cross, again from a corner. But all of a sudden Millwall were roused, team and crowd fired up by perceived injustice. For the first time, “No one likes us, we don’t care” could be heard from the stands. Aiden O’Brien saw a shot blocked when it was heading on target, Morison forced another block with a header from a corner and Zieler did well to hold on to a Shaun Williams effort. This game was still in the balance.

With 10 minutes remaining the best chance of the match fell to Okazaki, after a shot by the substitute Jamie Vardy deflected into his path. He tried to lift the ball over Archer but the keeper was smart enough to read the effort and blocked it strongly. Two minutes later Archer tipped Okazaki’s cross away from a pouncing Vardy.

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Then, with the match ticking towards added time, bedlam. A cross from Shane Ferguson found Lee Gregory on the edge of the box. The substitute, with his back to goal, played a beautiful blind pass through Leicester’s back four, where, of all people, the right-back Cummings was marauding forward. He collected the ball, shifted past a challenge and finished coolly with his left foot under Zieler. There was pandemonium on the pitch, in the dugout and in the stands.

Leicester desperately threw men forward but to no avail. The League One side, not the Premier League champions, would be advancing to the last eight.