United suffered a first defeat in 18 games but progressed to the EFL Cup final at Wembley despite a disappointing second-leg showing at Hull.
On manager Jose Mourinho's 54th birthday, the Reds started the contest with a two-goal lead that was halved through Tom Huddlestone's controversial penalty.
Paul Pogba's seventh of the season re-established our two-goal aggregate advantage, before Oumar Niasse's late goal restored the Tigers lead on the night.
That was not enough to change the outcome of the tie as the Reds set up a Wembley showdown with Southampton at the end of February, following the Saints impressive and deserved last four-victory over Jurgen Klopp's faltering Liverpool.
The hosts, rejuvenated under new boss Marco Silva, started brightly and went close twice early on through Harry Maguire and Sam Clucas.
Marcos Rojo had an effort deflected wide and David de Gea then thwarted Niasse at the other end at the culmination of a neat counter-attacking move.
In a season riddled with refereeing controversy, Jon Moss became the latest official to err when Rojo was harshly adjudged to have fouled Maguire following a corner.
Huddlestone made no mistake from the spot in the 36th minute but United almost provided an instant riposte when Zlatan Ibrahimovic forced a smart save from recalled Hull keeper David Marshall.
Having awarded Silva's side a very soft-looking penalty, Moss then compounded his error by ignoring two more obvious spot-kicks for United shortly after the interval.
Michael Dawson sent Pogba sprawling but the referee waved play on, and then Chris Smalling was bundled over by Huddlestone only for the protests to fall on deaf ears for a second time.
United were deservedly level in the 65th minute as Pogba poked home Marcus Rashford's pass to re-open the two goal lead.
Rojo headed against the bar and the impressive Niasse, on his first Hull start, did likewise at the other end.
The former Everton loanee got the goal his individual performance deserved when David Meyler picked him out to slam in from close range with ten minutes to play.
To their credit, the hosts showed admirable spirit and determination in the closing stages, but they were unable to find the goal needed to force extra time.
Having already won once at Wembley this season in the Community Shield, Jose has taken us back there in a bid for a fourth success in this competition.
Que sera sera!
Overall team perfomance: 5/10
United Faithful Man of the Match: Marcus Rashford.
NB: A special mention must go to the magnificent 4,179 United fans in the away end who did the team proud and never stopped singing. Simply incredible.