United went into the break leading 2-0, but Lyon fought back to level the game at 4-2 with ten men after Corentin Tolisso was sent off for two yellow cards. The mood inside Old Trafford changed from confidence to desperation, with the home fans booing their team.
In the most dramatic scenes, United scored twice in the last two minutes of extra time to win the game 5-4 on the night and 7-6 on aggregate. The final goal was a header from Harry Maguire, who played as a makeshift striker.
This victory was a lifeline for United, who will finish the season with their lowest points total in the Premier League era. Their fight and determination were on full display, and their fans will be asking why they couldn't show this same spirit during the regular season.
Goals from Manuel Ugarte and Diogo Dalot put United in the driving seat at half time, but Lyon came back strongly after the break. The French outfit's quickfire replies and time-wasting tactics left United looking nervous and disorganised.
With Lyon down to ten men, United seemed to have a chance, but extra time saw Lyon take the lead again. However, United's comeback was complete when Bruno Fernandes converted a penalty, Kobbie Mainoo levelled on 120 minutes, and Harry Maguire scored the winner.
This victory was as dramatic as the 1999 Champions League final, leaving United fans in utter disbelief. The end to the game was as thrilling as any sports fan could wish for.
Goalkeeper Andre Onana, who was recalled after missing the 4-1 defeat at Newcastle, made some fine saves but will still come under scrutiny for the four goals he conceded. Despite this, he celebrated long and hard at the final whistle.
United now await Athletic Bilbao in the Europa League semi-finals, and their fans will be hoping for more drama and excitement.