So Premier League Hull advance at the expense of Championship Newcastle. But this was not a simple story, one that included 120 minutes, a red card, a penalty shootout and goalkeeper heroics before Hull sealed a first League Cup semi-final place in their history.

Newcastle outplayed them for great periods of this match on a pitch that by the end was covered in frost and had been the stage for 90 minutes of dull football followed by 30 compelling ones.

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Neither side could find a breakthrough in normal time and, when Dieumerci Mbokani was sent off in the 89th minute, Hull looked down and out. Mohamed Diamé put Newcastle in front in extra time before Robert Snodgrass equalised one minute later and the game went to penalties. Newcastle missed three with Eldin Jakupovic saving two – Jonjo Shelvey, Dwight Gayle and Yoan Gouffran the culprits – while Hull finished theirs emphatically.

Mike Phelan, the Hull manager, said: “I thought Newcastle played decent football and moved the ball around well but I thought we were also good value for money tonight. For this football club it’s a tremendous achievement because it’s the furthest they’ve ever been [in the competition]. The players are really pleased with that.

“I was pleased for all of them. Eldin has been in the cup competitions all the way through and has performed well. Going into the penalty shootout he was probably the right goalkeeper to have there. He’s probably been the hero tonight and hopefully he’ll be the hero again.”

Diamé looked as if he had won this tie in the 98th minute and is a player who reflects these two teams’ unusual status. Promoted with Hull last season – scoring the winning goal in the Championship play-off final, indeed – he rejected a contract offer from City and opted to drop down a division with Newcastle.

The Senegal international was a key figure in a first half that Newcastle dominated. Shelvey played an exquisite through-ball to Gayle in the 12th minute, which the striker controlled with ease before releasing a powerful left-footed shot that Jakupovic palmed away. Gayle, who has scored 13 league goals this season, returned to the Newcastle starting XI after being a late substitute in the home defeat against Blackburn Rovers and was one of seven changes for the visitors. Hull made six.

Facebook Twitter Pinterest Eldin Jakupovic takes the acclaim of the Hull City fans after his penalty shootout heroics. Photograph: Lee Smith/Reuters

With the away end packed and the black and amber shirts providing little warmth early on for the Hull supporters on a bitterly cold evening, all the initial noise emanated from Newcastle’s contingent. Rafael Benítez had argued before this game that the club should have been given more tickets but those who got them certainly made their presence felt.

Newcastle controlled the tempo in the first half and Isaac Hayden, in particular, impressed in the centre of midfield. Hull attempted to change the momentum as the game wore on and, although there was little cohesion going forward, they did begin to edge back into things. Andy Robertson darted forward from left-back and cut inside, only for Hayden to barge him off the ball and concede a free-kick. Snodgrass curled an effort towards Matz Sels’ left-hand post but the goalkeeper calmly watched it go wide.

The drama was saved for the dying moments of normal time. Jamaal Lascelles challenged Mbokani from behind on the touchline in front of the Hull dug-out, the pair tangling legs and the striker visibly riled. They then went head to head and Mbokani moved his forward with more force, earning a red card from Neil Swarbrick. It was hardly a headbutt but there was movement towards Lascelles.

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That proved the final act of the 90 minutes and in extra time Newcastle began to make their numerical advantage count. Achraf Lazaar ventured forward from left-back and smashed a shot against the bar from inside the Hull penalty area before Diamé gave the visitors the lead. A corner was taken short to Vernon Anita on the right of the penalty area and his clipped cross was flicked on by Gayle to Diamé, who prodded into the bottom corner.

This sparked mass celebrations in the away end but the party did not last long. One minute later Hull were level. A long ball forward from defence was headed on by the substitute Markus Henriksen, who then unleashed a fierce effort at goal. It was straight at Sels but he could only palm the ball out to the onrushing Snodgrass who slotted it in underneath the goalkeeper.

Benítez said: “There are a lot of positives because the team was doing well. In the second half they [Hull] were pushing and we defended well. We allowed them to play the counterattack and we have to improve that. As a team we made mistakes.

“We allowed them to score. It’s not the keeper’s fault. We have to carry on working hard and doing things in the same way.”

Hull were emphatic with their penalties, Snodgrass, Michael Dawson and Huddlestone all scoring to send them into the last four.