Just three out of 10 spot kicks were scored as Sunderland secured their place in the final with a 2-1 victory on penalties, after United had forced the issue by winning the second leg 2-1 after extra-time to make the aggregate score 3-3.
A goal deep into extra-time from former United man Phil Bardsley appeared to have put Sunderland into the final but the visitors were made to wait when Javier Hernandez's even later strike for United sent the match to spot kicks.
United had taken the lead in the 37th minute, when Adnan Januzaj put a corner over from the right and Danny Welbeck miss-hit a first-time shot which bounced up and found the head of Jonny Evans at the far post. The defender headed in unmarked, having lost the Sunderland defender assigned to him.
Sunderland were much the better side in the second half, providing most of the attacking threat as United curiously seemed to be happy to hang onto their lead on the night. Indeed, as the game went into extra-time, they seemed to actively start wasting time, as at that stage they were heading through on away goals.
However, with a minute to go Salford-born and bred Bardsley lined up a shot which went straight at David De Gea, and the United keeper somehow let the ball slip through his fingers and into the corner of the net.
Sunderland thought they were through, but then Januzaj made space on the left side of the box, crossed low and the ball eventually found Hernandez at the far post, who stabbed into the roof of the net.
The game went to penalties, almost all of which were awful. Craig Gardner and Welbeck blazed the first two over, and Steven Fletcher's was weak and saved, before Darren Fletcher finally scored one, but only just.
Marcos Alonso levelled things up before Januzaj's tame effort was saved and Ki put Sunderland ahead with the next kick. Phil Jones then missed, followed by Adam Johnson, leaving Rafael the task of scoring to keep United in the game.
However, Mannone saved, putting Sunderland into the final, where they will play Manchester City.
37' - GOAL - EVANS GIVES UNITED THE LEAD - Januzaj puts a corner over from the right, Welbeck miss-hits a first-time shot which bounces up and finds the head of Evans at the far post, where he heads in unmarked.
119' - GOAL - BARDSLEY THINKS HE'S PUT HIS TEAM IN THE FINAL - Incredible scenes, and what a mistake by David De Gea. The ball breaks to Bardsley on the edge of the area, he hits a low shot straight at the United keeper, who somehow allows it to slip through his fingers and into the corner.
121' - GOAL - HERNANDEZ SENDS THE MATCH TO PENALTIES - Januzaj does brilliantly and plays a one-two, then puts a low cross in that Hernandez stabs in. Penalties ahoy.
PENALTY SHOOT-OUT - Mannone saves from Rafael to settle one of the worst penalty shoot-outs ever witnessed.
Sunderland had only one shot on target in the whole 120 minutes - their goal.
However, they did have 54% of the possession.
Sunderland had 18 shots off target, while United had 19.
Yet more woe for David Moyes. It's impossible not to feel sorry for Moyes, sometimes. Had the usually reliable De Gea gathered a routine shot with a minute of extra-time to go, United would be in a cup final and have something of a silver lining on what has been a dreadful first season so far. As it is, he has more problems to deal with. Knowing his luck, Juan Mata will turn out to have a degenerative knee condition and that move will be called off tomorrow.
MAN OF THE MATCH
Adam Johnson (Sunderland): He's a frustrating and inconsistent sort, but more or less everything threatening Sunderland did came through Johnson, drifting from the right into the centre and providing cross after cross. He missed his penalty, but then again he wasn't alone in being terrible from 12 yards, so it would seem silly to single him out for that. He now gets the chance to face his former employers Manchester City in the final.
MANCHESTER UNITED: De Gea 4; Rafael 6, Smalling 7, Evans 7, Buttner 5, Kagawa 5, Carrick 6, Fletcher 6, Januzaj 7, Welbeck 6, Hernandez 5. SUBS: Evra 5, Jones 5, Valencia 6.
SUNDERLAND: Mannone 6, Bardsley 7, Alonso 5, Brown 6, O'Shea 5, Cattermole 5, Colback 6, Ki 7, Johnson 8, Borini 6, Fletcher 6. SUBS: Gardner 6, Altidore 4.
THE MATCH IN A TWEET