Marcus Rashford scored an added-time penalty to send Man Utd through to the quarter-finals of the Champions League on away goals at the expense of PSG.
In what was a thrilling contest at the Parc des Princes, Romelu Lukaku scored two first-half goals following two individual errors from the Parisians - one from Thilo Kehrer and one from Gianluigi Buffon - to hand United hope of becoming the first side to overturn a 2-0 home first-leg deficit in a knockout round.
But Juan Bernat's 12th-minute goal looked to have handed PSG what they needed to run out aggregate winners - until United were handed, via Video Assistant Referee (VAR), a 94th-minute penalty for handball by Presnel Kimpembe.
Rashford converted the spot-kick to secure a 3-1 (3-3 aggregate) win for United on the night - and hand Ole Gunnar Solskjaer a famous win which surely will strengthen his case of being made United's permanent manager.
Scoring the first goal at the Parc des Princes seemed to be on the minds of both managers in the build-up to this round of 16 second-leg clash on Wednesday night.
Indeed, both Solskjaer and Tuchel had said that scoring the opener could prove crucial to determining which team progressed to the quarter-finals.
But even Solskjaer couldn't have dreamed of seeing his United side score after just two minutes - even if it came following a dreadful mistake by Thilo Kehrer.
The 22-year-old, who had told reporters a day earlier the hosts were confident of beating United, saw his backpass latched onto by Lukaku who, despite taking a heavy touch, was able to drive it into the back of the net from a tight angle.
With the goal coming after just 1 minute and 51 seconds, Lukaku's strike was the fastest scored by United in a Champions League knockout match since Wayne Rooney netted against Bayern Munich nine years ago.
You just keep a cool head, they're the type of things you practice. I wanted to take it."
It was the perfect start for United, but PSG remained remarkably cool and responded just 10 minutes later thanks to some brilliant work by Mbappe down the right flank.
His cross flew across the United box and was fired past David De Gea by the incoming Juan Bernat to restore PSG's two-goal lead in the tie.
United had certainly started well despite a much-changed line-up due to injuries and Paul Pogba being suspended.
But what became evident, very quickly, was how much Eric Bailly was struggling playing at right-back.
Time and time again, he was bypassed by Bernat and co.
It would surely have been embarrassing had Solskjaer taken the right, but difficult, decision to haul him off early but, in the end, the United boss was handed the excuse he was looking for when Bailly appeared to pick up a knock in the 35th minute.
However, the substitution came after the defender played a role in United's second goal of the night - which followed yet another individual mistake by the hosts.
This time, it was veteran goalkeeper Gianluigi Buffon who spilled the ball after Marcus Rashford had struck at him, thereby allowing Lukaku to drive in from close range.
United had just 24.1 per cent possession in the first half but, whenever they surged forward, they looked dangerous and, indeed, Buffon suffered another nervy moment when Diego Dalot, Bailly's replacement, saw his attempted cross take a heavy deflection and fall, just about, into the PSG goalkeeper's arms.
Man Utd Player Ratings
By James Robson
De Gea 7
Bailly 3
Smalling 9
Lindelof 9
Young 8
McTominay 9
Pereira 5
Fred 7
Shaw 7
Lukaku 9
Rashford 8
Substitutes
Dalot 6
Chong 5
Greenwood N/A
The second half proved to be less entertaining but, equally as enthralling, as United were far more compact and sat back more and waited for PSG to slip up.
The visitors were let off the hook when their former winger, Angel Di Maria, saw his 59th-minute chipped effort over De Gea chalked off for offside.
Shortly after PSG had rattled the woodwork, Solskjaer sent on 17-year-old Mason Greenwood for his United debut.
But the academy graduate couldn't score what would have been the crucial away goal for the visitors, though another graduate did in the form of Rashford.
After VAR was used to award a late spot-kick, Rashford coolly converted it to silence the home crowd and leave the travelling supporters in ecstasy.
Line-ups, match highlights and reaction
PSG: Buffon, Kehrer, Thiago Silva, Kimpembe, Bernat, Verratti, Marquinhos, Dani Alves, Draxler, Di María, Mbappe
Substitutes: Areola, Paredes, Cavani, Meunier, Choupo-Moting, Kurzawa, Dagba
Man Utd: De Gea, Young, Bailly, Smalling, Lindelof, Shaw, McTominay, Fred, Pereira, Rashford, Lukaku
Substitutes: Romero, Dalot, Rojo, Garner, Gomes, Chong, Greenwood
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