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Leicester were keen to test the Hull defence in the opening stages of the match as Andrej Kramaric unleashed a powerful strike from distance just moments after kickoff, but he was unable to test the keeper.
The home side started to see more of the ball as the first half progressed, but Ritchie de Laet was on hand to make the clearance after Mohamed Diame and Shaun Maloney charged forward, while Mark Schwarzer claimed a high ball into the box from Tom Huddlestone.
The Foxes finished the first half on the front foot, though, as Kramaric made a break down the left before crossing in for Joseph Dodoo, who had scored in both of Leicester's League Cup fixtures before tonight, but Andrew Robertson headed it clear.
Diame was on the move for the hosts at the start of the second half as he tried to get a cross in from the right, but Ben Chilwell was able to stop the ball from reaching its target.
There was a moment of concern down the other end for the home side soon after, though, as Eldin Jakupovic spilled the ball while trying to clear a Marc Albrighton delivery, but his defenders were able to scramble it clear.
With Diame continuing to dictate the game, the Premier League side made changes just after the hour mark as top scorer Jamie Vardy and Danny Drinkwater came on, with the former attempting to set up Dodoo shortly after his introduction, but the finish was wide.
Albrighton made a run down the right inside the final 10 minutes before trying to find Vardy with a cross, but Jakupovic beat the striker to the ball.
Hull thought that they had opened the scoring down the other end less than two minutes later as Schwarzer was unable to hold onto an Abel Hernandez header, resulting in the home side claiming that the ball was over the line, but the referee was not convinced.
Schwarzer was tested again moments later after Michael Dawson nodded the ball into the path of Hernandez, but his volley was comfortably held by the Australian keeper.
With both sides unable to break the deadlock inside 90 minutes, the match went to extra time, with Albrighton trying to find an early goal for the Foxes, but Vardy could not connect with his free kick from out wide.
Leicester finally opened the scoring in the 100th minute when Vardy raced into the box, forcing a save from Jakupovic, but Riyad Mahrez was there to poke the rebound over.
The home side were level just five minutes late with a similar goal to Leicester's opener, as Hernandez converted after Schwarzer parried a strike from Chuba Akpom.
Neither side could find a second goal, so the match went to a penalty shootout, with Hull immediately getting the advantage as Jakupovic tipped Mahrez's spot kick onto the post.
Maloney and Hernandez both scored their penalties for the home side to ensure that they led 2-1 after the first four, before both sides converted their next two, leaving Vardy needing to score the fifth for Leicester, but David Meyler made it five out of five for Hull to send the Championship side through.