United’s season looked over when Lyon came from 2-0 down to lead by two goals with just six minutes remaining at Old Trafford despite having captain Corentin Tolisso sent-off.
However, a Bruno Fernandes’ penalty, Kobbie Mainoo’s strike and Harry Maguire’s header capped a stunning finale to set up a semi-final meeting with Athletic Bilbao.
The Red Devils sit 14th in the English top flight and defeat would have almost certainly meant missing out on European football entirely next season.
Instead they are just three games away from a European trophy and the lifeline of direct access to the riches of the Champions League next season.
First-half goals from Manuel Ugarte and Diogo Dalot had put United in a commanding position.
But the defensive deficiencies and mental fragility of Ruben Amorim’s side were exposed in a collapse that threatened to cap a miserable campaign.
Two goals in seven minutes from Corentin Tolisso and Nicolas Tagliafico brought Lyon level.
Tolisso was then sent-off for two yellow cards in the 89th minute.
The 10 men still looked set to prevail in the extra 30 minutes thanks to a brilliant strike from Rayan Cherki and Alexandre Lacazette’s penalty.
United’s history is build on dramatic late fightbacks but few have been more remarkable than this to leave Lyon shellshocked.
The home side got off to a flying start thanks to a fine team goal as Fernandes released Alejandro Garnacho down the right and his cross picked out Ugarte to slot in just his second goal since joining the English giants form Paris Saint-Germain.
Amorim’s decision to restore Andre Onana in goal was under scrutiny.
The Cameroonian had been dropped for Sunday’s 4-1 thrashing at Newcastle after two costly errors that led to both Lyon’s goals in last week’s 2-2 first leg draw.
Those mistakes came after a war of words with former United midfielder Nemanja Matic, who labelled him “one of the worst goalkeepers in United’s history.”
The 29-year-old rewarded his manager’s faith with a couple of important stops to prevent Lyon levelling through Paul Akouokou and Cherki.
At the other end, a United side that have often looked laboured and lacking in ideas all season, suddenly clicked into gear in the first 45 minutes.
United doubled their lead in first-half stoppage time when Maguire’s long ball was expertly controlled by Dalot, who then fired in off the inside of the post.
Garnacho should have killed the tie off within minutes of the restart for the second half when he shot straight at Lucas Perri with Fernandes begging for a pass for a tap in.
That was to prove a turning point as United crumbled in stunning fashion.
Lyon boss Paulo Fonseca was able to prowl the touchline unlike in Ligue 1 where he is serving a nine-month touchline ban.
The Portuguese introduced captain Lacazette off the bench in a bid to turn the tide.
And the former Arsenal striker played a central role in the fightback.
Lacazette flicked on Moussa Niakhate’s header and Tolisso swooped to head in and give the visitors a lifeline.
Tagliafico then prodded in at the back post despite Onana’s attempt to scoop it off the line.
Just as Lyon were in the ascendency Tolisso gave them a mountain to climb again with a soft second yellow for a trip on Casemiro.
Yet, it did not initially matter as Cherki confirmed his status as one of Europe’s rising stars with a powerful drive that left Onana motionless.
Lyon’s other prized asset Malick Fofana was then chopped down by Luke Shaw inside the area and Lacazette confidently dispatched the resulting spot-kick.
Another penalty at the other end, though, kickstarted the fightback as Fernandes fired home.
Substitute Mainoo showed why he had been thrust in an unfamiliar forward role with a composed finish to level on 120 minutes.
Barely 60 seconds later Maguire completed the comeback with a towering header at the back post. (AFP)
