Marcus Rashford struck a last-gasp penalty as United made UEFA Champions League history.
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Marcus Rashford converted a 94th-minute penalty as Manchester United completed a historic comeback to snatch a place in the quarter-finals from Paris Saint-Germain's grasp.
No side had ever recovered from a 2-0 home defeat in the UEFA Champions League knockout stages but Romelu Lukaku's goal inside two minutes set the visitors on course for a famous triumph.
For Paris, it brings back painful memories of Barcelona's remarkable 'remontada' two years ago. Juan Bernat's reply restored a sense of calm but an uncharacteristic fumble from Gianluigi Buffon let Lukaku in for his second on the half-hour mark.
Still PSG rarely looked troubled at the back, Bernat hitting the post at the other end, until deep into added time Presnel Kimpembe was adjudged to have handled following consultation with VAR. Rashford did the rest.
View from the stadium: Chris Burke
Absolutely incredible. United are through after a fightback to rank among the club's very finest – and they're hardly short of those. So much credit goes to Ole Gunnar Solskjær and his charges for making this a contest to begin with, and then pulling off a result almost no one predicted. As for Paris, yet another round of recriminations is set to commence. Thomas Tuchel clearly hasn't got their knack for European collapses out of the system just yet.
Man of the match: Romelu Lukaku
Rashford showed incredible composure from the penalty spot in second-half stoppage time, but United wouldn't have been in that position had it not been for Lukaku, whose third double in as many appearances laid the foundations. The Belgian didn't have many opportunities but made the most of the chances that came his way to help clinch the Red Devils' place in the last eight.
1: United are the first side in European Cup history to overturn a 2-0 home defeat in the knockout stages.
2: United are the first team to progress in the UEFA Champions League after losing the first leg of a knockout tie at home by two or more goals (34 previous cases).
4: United are through to the quarter-finals for the first time since 2014, a five-year absence.
11: United have won only two of their last 11 UEFA Champions League knockout phase matches.
17: At 17 years and 156 days, Mason Greenwood became the youngest player to appear for United in the UEFA Champions League, breaking the record of Gerard Piqué.
21: United have scored in 21 consecutive away matches in all competitions, equalling the club record set in 1956 and 1957 under Sir Matt Busby.
24: Paris have scored in each of their last 24 UEFA Champions League games.
What does it mean?
Solskjær's Midas touch shows no sign of abating. This was his 14th win in 17 matches since he was parachuted in to replace José Mourinho in December. He wore a bib throughout in Paris, inviting thoughts of him reprising his super-sub act of old, but he has a new role now and he seems pretty adept at it too. United will fear no one in next Friday's draw: their manager wouldn't allow it.
United have an important fixture on Sunday in the race to finish in the Premier League's top four – a visit to fellow hopefuls Arsenal. Solskjær's side then travel to Wolves in the FA Cup quarter-finals the next weekend, ahead of the quarter-final first leg in the second week of April.
The double is still on for Paris. Prior to the international break they go to Dijon and entertain longstanding rivals Marseille. Tuchel's troops then head to Toulouse and welcome Nantes (a French Cup semi-final) and Strasbourg.