Korey Smith struck deep into injury time as Championship high flyers Bristol City knocked out the holders and sent the Robins into
Lee Johnson's side had beaten three Premier League sides en route to the last eight in the shape of Stoke, Watford and Crystal Palace. They took the scalp of United to make that five and set up only a second ever major semi final where they will face Pep Guardiola's Manchester City.
Zlatan Ibrahimovic's free-kick - his first goal since his return from an eight month lay off - cancelled out Joe Bryan's exquisite opener. The quarter-final tie seemed set for extra-time until Smith smashed high beyond Sergio Romero with an angled finish that sent Ashton Gate into delirium.
United can consider themselves unlucky to go out, having struck the post and the bar through Ibrahimovic and Marcus Rashford. City were also indebted to ex Reds keeper Luke Steele who produced several smart saves to keep an almost full-strength United side at bay.
Romero saved well from Josh Brownhill early on but United knocked on the door early on and almost went ahead after 18 minutes when Anthony Martial picked out Ibra and his effort deflected onto the bar and rebounded to safety.
City threatened again when Marlon Pack was headed towards goal by Nathan Baker, but Daley Blind cleared well from under the bar. Rashford was then very unfortunate not to put United ahead with a shot from distance, when his 30 yarder thudded back off the post with a scrambling Steele beaten.
Romero saved superbly from Hordur Magnusson before Aden Flint had the ball in the net, but his effort was chalked out for a foul on the Reds stand-in stopper. The hosts ended the half strongly, and Blind was again required to save his side with a superb last-ditch challenge on Smith as he looked poised to score.
The Robins took the lead within six minutes of the second-half restart when Pack picked out Bryan who thumped home off a post with a stunning finish beyond Romero. Parity was quickly restored, though, when Ibra's clever free-kick went under the wall and in with the aid of a slight deflection seven minutes later.
United pushed for a winner with Rashford denied by an inch-perfect challenge by Bryan, before substitute Romelu Lukaku forced Steele into two superb diving saves with a header and a low drive.
It was to be the hosts who would claim a famous victory, however, as Smith's close-range finish prompted scenes of wild celebrations from the jubilant home fans with a pitch invasion at full-time.
United Faithful Man of the Match: Marcus Rashford
Overall team performance: 6/10