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.