Eldin Jakupovic was 10-man Hull's hero as they beat Newcastle 3-1 on penalties in the EFL Cup after the quarter-final tie had finished 1-1 at the end of extra time.
Tigers goalkeeper Jakupovic kept out Jonjo Shelvey's spot-kick and also saved from Yoan Gouffran, while Dwight Gayle's effort hit the crossbar.
Hull trio Robert Snodgrass, Michael Dawson and Tom Huddlestone all converted their penalties to secure Mike Phelan's side an unlikely passage into the last four of the competition for the first time in the club's history.
Newcastle looked to have earned themselves a deserved win in extra time when Mo Diame scored against his former club, but Snodgrass levelled within a minute for the Tigers, who had Dieumerci Mbokani sent off in the 89th minute.
Newcastle carried the greater threat in the first half and had a penalty appeal turned down by referee Neil Swarbrick when Gayle went tumbling under Ahmed Elmohamady's challenge.
Gayle forced Hull goalkeeper Jakupovic to turn away a sweetly-struck half-volley after being set free by Shelvey's brilliant pass and Diame pulled a low shot wide.
Snodgrass crashed Hull's first effort on goal wide in the 23rd minute, but Newcastle twice went closest to breaking the deadlock moments later when Diame headed Vurnon Anita's cross inches over and Matt Ritchie's superb first-time effort curled wide following a short corner.
Barring a brief flurry from the home side after the interval, Newcastle assumed control again, dictating both possession and the tempo.
But with an hour gone Benitez's side had nothing to show for their efforts and after David Meyler had pulled a shot wide, Hull enjoyed their best period of the match.
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Snodgrass' free-kick from striking range hit the wall and after left-back Andy Robertson's storming run to the edge of the area had been halted illegally by former Hull loanee Isaac Hayden, the Scot went closer with another free-kick from a similar position.
Shelvey scuffed his shot well wide after gliding into the box and Robertson just failed to get on the end of Snodgrass' pass at the other end - with 20 minutes to go the cup tie was still waiting for a spark.
Tigers boss Phelan sent on Markus Henriksen, teenager Josh Tymon and James Weir for Jake Livermore, Robertson and Elmohamady with 11 minutes to go and soon after Christian Atsu replaced Newcastle midfielder Ritchie.
But the pattern never changed. Newcastle probed and Hull hung in doggedly, aided by their visitors' failure with the final delivery and the odd foray forward themselves to ease the pressure.
Hull were reduced to 10 men as the tie headed towards extra time. Mbokani reacted furiously to Jamaal Lascelles' tackle from behind and referee Swarbrick showed the DR Congo international a straight red card.
Newcastle sniffed blood. Defender Ciaran Clark's shot was well blocked by Jakupovic, who then kept out Shelvey's thunderbolt.
But the Hull keeper could do little to keep out Diame's opener. Gayle flicked on Anita's cross and the summer signing turned the ball home at the far post.
Hull then delivered a stunning riposte, hardly in keeping with the contest. The Tigers swept forward soon after the restart and when Henriksen's thumping drive from the edge of the area was parried by Sels, Snodgrass pounced to steer home the rebound.
Both sides spurned chances to win it in the second period of extra time.
Gayle's header was kept out by man-of-the-match Jakupovic, Lascelles' shot was blocked by Hull skipper Dawson and at the other end Snodgrass failed to get a shot away after being sent one-on-one with Sels by Diomande.
