Marcus Rashford belted home the stoppage time penalty past PSG goalkeeper Gigi Buffon to give the visitors a 3-1 triumph and the crucial third away goal which sent them through to the last eight for the first time since 2014.
It was a vignette worth a place in the Solskjaer scrap book that includes a last minute winner in the 1999 Champions League final against Bayern Munich.
"Fearless," said Solskjaer of Rashford's poise after the 21-year-old had to wait several minutes amid whistles and PSG gamesmanship before taking the penalty.
"He's got no doubt and no fear," the Norwegian added. "When you're young you don't have any fear. I wasn't sure he was going to score. But he slotted it in. Brilliant."
"That's what we do" could be just as easily applied to PSG who for the third consecutive season went out of the Champions League in the last 16.
In 2018, Real Madrid beat them on their way to their 13th European crown and in 2017, Barcelona, four down after the first leg at the Parc des Princes, pulverised Unai Emery's men 6-1 at the Camp Nou to advance 6-5 on aggregate.
PSG's Qatari owners dispensed with Emery for his shortcomings in European club football's most prestigious competition even though he had harvested six domestic trophies including a treble of Ligue 1, Coupe de France and League Cup in 2018.
Thomas Tuchel, his replacement, has mirrored his predecessor in the Champions League but won't be able to rival him in national competitions with PSG out of League Cup.
Where did it all go wrong?
They are 17 points clear in the race for the 2019 French title and in the last eight of the Coupe de France.
But in Europe? It's not working. And it's hurting with the best part of a billion euros spent on an obsession to join the aristocrats such as Real Madrid, Barcelona and Bayern Munich. Even parvenus such as Chelsea have won the Champions League.
"It's always hard to lose and to accept," mourned Tuchel. "But if you're up against an opponent who is having a top day and big qualities and in some situations is clearly better, then you can accept it because you have something to analyse but we did not deserve to go out after 180 minutes, not at all."
The French sports daily L'Equipe said PSG's exit was lamentable given the weakness of a United team missing France international midfielder Paul Pogba due to supsension and nine other players through injury.
It said responsibilty for the elimination went right up to the top of the club hierarchy.
Inquests and conquests, however, are the very soul of elite football and while a resurgent Manchester United throb bonhomie and potential, PSG are benighted and sunk in their slough of despond.
"We have to be very careful not to make hasty decisions," warned Tuchel. "You can't start pointing the finger at players and blaming them.
"We've got to play the same way ... and normally we'd win or draw. But you look at the result and think we didn't play well. It is not a logical result."
Football, Thomas, bloody hell.