Hull City 2-1 Manchester United (Agg: 2-3)
Manchester United set up an EFL Cup final against Southampton despite their 17-match unbeaten run ending with defeat at Hull City in the semi-final second leg on Thursday.
Jose Mourinho's side led 2-0 from the first leg but, making five changes, they struggled to impose themselves at the KCOM Stadium.
Tom Huddlestone put the hosts ahead from the penalty spot after four players had tangled in the area after a set-piece, Marcos Rojo's pull on Harry Maguire's shirt the most visible offence.
It gave Hull, 19th in the Premier League, poise and confidence, but their hopes of just a second domestic cup final in their 113-year history were dashed when Paul Pogba poked through the legs of Maguire and into the bottom corner from 10 yards.
Rojo headed against the bar for United and the Tigers' Oumar Niasse also struck the woodwork before he turned in David Meyler's cross to set up a tense finale.
But the visitors held on and former Chelsea boss Mourinho could move level with Brian Clough and Sir Alex Ferguson on four League Cup wins at Wembley on 26 February.
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Happy birthday Jose
Former boss Ferguson said earlier in the week that Mourinho had "got to grips" with the managerial role at Old Trafford - and a major final will surely only further build confidence as United remain in the hunt for a Champions League qualification berth and in three cup competitions.
The EFL Cup may not top the list of objectives for Red Devils fans, but their team have shown a hunger to beat three Premier League teams on the way to Wembley in Hull, West Ham and Manchester City.
On his 54th birthday, Mourinho shuffled his pack. Marcus Rashford and Jesse Lingard were preferred to Juan Mata and Henrikh Mkhitaryan and United were deservedly beaten.
There were contentious moments, notably the penalty award which BBC Radio 5 live pundit Ally McCoist deemed "soft" and United had calls for their own spot-kick when Chris Smalling went down under Tom Huddlestone's challenge after the break.
Mourinho seemed irked by officiating after the match, but on the night his side had less of the ball, fewer shots than their hosts and were probably asked to work far harder than he would have liked.
There were positives. Marcus Rashford's pace on times troubled the hosts, Zlatan Ibrahimovic showed touches of flair - notably when bringing a fine save from David Marshall - and most importantly, United will bid for a fifth League Cup win.
However, with progress comes dilemmas. Mourinho will now see the depth of his squad tested, with the final arriving on the same day United were scheduled to face Manchester City in the league and four days after the second leg of a Europa League tie at Saint-Etienne.
Could Hull stay up?
Hull, on paper at least, stood no chance before kick-off. On 26 of the 27 previous occasions a side had lost a League Cup semi-final first leg by two or more goals they have gone out.
But ploughing on through adversity is a necessary pre-requisite at the KCOM Stadium.
Robert Snodgrass - who has created 30 more chances than any other Hull player this season - was left out amid two bids for his services, midfielder Jake Livermore has been sold and recent acquisition Ryan Mason will likely face a long lay-off after fracturing his skull. All things considered, this was a display to be applauded.
The fact the starting line-up included four players who have each played less than five games this season in Shaun Maloney, Jarron Bowen, Niasse and Josh Tymon, perhaps underlined coach Marco Silva's priorities.
But Bowen was neat and tidy, while Everton-reject Niasse proved a constant nuisance. The experience of Tom Huddlestone was key as he picked intelligent passes in midfield and new recruit Lazar Markovic came off the bench to help craft the second goal.
With Hull's league position so precarious, would the distraction of a cup final proved a nuisance for Silva?
He has a bigger battle to fight but this win showed that even with key names out, he has a squad which may have the character needed for a successful scrap against the drop.
'Wembley's special meaning'
For all the Hull vigour, semi-finals belong to winners and United will now compete in their ninth League Cup final.
Victory in this competition of course kick-started Ferguson's success in 1992, and a quarter of a century on Mourinho will bid to maintain his unbeaten run in League cup finals.
"Wembley is Wembley, it is for professionals with passion for football. It has a special meaning, a special feeling," said the United boss.
Man of the match - Oumar Niasse
'I behaved on the bench' - what the managers said
Hull manager Marco Silva: "It was a good win but not enough for our goal. It is important to win the game but the result in the first leg caused problems for us. It was a good performance again, a good attitude and we controlled the game in large periods against a big team. It is impossible at this moment to feel really happy.
"The goal we conceded is not a normal goal, we lost control at the vital moment."
Manchester United boss Jose Mourinho: "I just want to say congratulations to my players. It was a difficult road to be in the final and we are in the final. I don't want to say anything else. It is enough, I am calm, I behaved on the bench, no sending off, no punishment so no more words."
Home fortress - the stats you need to know
- Manchester United have reached their ninth League Cup final - second only to Liverpool in the history of the competition (12).
- Paul Pogba scored his seventh goal of the season in all competitions - only Zlatan Ibrahimovic has more for the Red Devils this season (19).
- Tom Huddlestone's penalty was his first goal in 31 games in all competitions for the Tigers, while Oumar Niasse scored his first goal in English football (11th game).
- This was Jose Mourinho's first ever defeat at the hands of the Tigers (W6 D0 L1).
- Hull have won their last three home games in all competitions, having won just two of their previous 11 at the KCOM Stadium this season.
Manchester United host Wigan Athletic in the FA Cup on Sunday in a 16:00 GMT kick-off, after Hull travel to meet Fulham in the competition at 12:30.