An injury-ravaged United squad travelled to face Paris without ten first team players, but caused a huge upset.
Two first half goals from Romelu Lukaku put them in a promising position, despite Juan Bernat scoring for the hosts.
As the game wore it looked like United would fall valiantly short, before VAR controversy awarded them a spot kick at the death.
Presnel Kimpembe was adjudged to have handled in the box, allowing Marcus Rashford the chance to slam home a late winner.
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Heroic United shock Europe
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Most had written off United's chances of progressing any further after the damaging first leg defeat at Old Trafford.
But a valiant effort from Solskjaer's side took them within a whisker, before Rashford's penalty earned them the win.
United were without nine injured players, whilst Paul Pogba was missing with suspension.
That prompted Solskjaer to go with a midfielder three of Scott McTominay, Andreas Pereira and Fred, whilst his bench was packed full of youth team players.
And against all odds the Red Devils still progressed with one of the historic results in their history.