After a scoreless first-half and a goal each in extra-time, Mike Phelan's side secured their place in the last four with a penalty shootout win
Eldin Jakupovic saved two spot-kicks as 10-man Hull City progressed to the semi-finals of the EFL Cup for the first time after defeating Newcastle United 3-1 on penalties.
With the quarter-final tie ending 1-1 following 120 minutes, Jonjo Shelvey and Yoan Gouffran were both denied by Jakupovic in the shootout, where Dwight Gayle saw his effort hit the crossbar.
Robert Snodgrass, Michael Dawson and Tom Huddlestone all converted for hosts Hull to send them through to the last four.
Former Hull hero Mohamed Diame – who scored the only goal to settle last season's Championship play-off for the Yorkshire side - had earlier broken the deadlock when he struck in the first half of extra-time
However, the Tigers hit back instantly in the 99th minute through Snodgrass, with the midfielder quickest to react to slow defending from Rafael Benitez's men when scrambling home a rebound.
Dieumerci Mbokani was sent off for Hull in the closing stages of normal time following an incident with Jamaal Lascelles, but the numerical disadvantage mattered little, thanks in part to Jakupovic's heroics.
The two sides had a combined 13 changes to their starting line-ups following their respective last league games, and Newcastle made the more confident start with Gayle forcing a smart save from Jakupovic in the 14th minute after Shelvey's throughball.
Moments later, with the visitors backed by a vocal away following, Diame rolled a shot narrowly past the far post from outside the box.
The home side were largely under the cosh and struggled to create, but in the 23rd minute Snodgrass hit a half-volley wide, while at the other end Diame rose highest to nod a Vurnon Anita cross over.
Matt Ritchie fired another warning shot three minutes later, striking a vicious effort from the edge of the box that failed to dip under the crossbar quickly enough. Another former Hull man in Isaac Hayden also saw an effort from distance clip the outside of the post just after the half-hour mark.
The second half was much less eventful than the first, but Hull began to claw their way back into the game, the highlight of their chances being a Snodgrass free-kick whipped past the far post in the 64th minute.
Mbokani was given his marching orders with two minutes left in normal time after he appeared to force his head into Lascelles, making a physical game even tougher for Mike Phelan's side.
Newcastle had the best of the early exchanges in extra time and went ahead after a period of pressure. After Achraf Lazaar had hit the crossbar and Shelvey had seen an effort saved moments earlier, Diame was on hand to convert from close range after Gayle's flick on.
The joy would be short-lived, however, as Snodgrass tucked home a rebound from substitute Markus Henriksen's low shot.
Gayle tested Jakupovic in the early stages of the second period of extra time when he headed goalwards from Christian Atsu's cross, while Snodgrass had a chance to steal the headlines but fluffed his lines after being put through on goal.
Jakupovic then saved Shelvey's penalty and Gayle hit the bar before Gouffran was also denied as Newcastle missed three penalties of four to be eliminated.