Having a good run in the Premier League is one thing, but doing it against the big boys at the sharp end of the Champions League is something else. Momentum can take a team only so far and Tuchel, the highly rated former Borussia Dortmund coach, showed the need to be tactically astute to win on a stage as unforgiving as the Champions League knockout rounds.
Kimpembe was left completely unmarked to side-foot home Di Maria's corner from point-blank range on 53 minutes.
He said: "Today we weren't at the level".
A 2-0 victory in the Champions League - consigning Solskjaer to the first loss 12 games under his caretaker command - was produced by PSG on Tuesday without two of the French club's fearsome forwards.
Former United winger Di Maria, booed from the outset by sections of the crowd, had the last laugh when he collected a fine pass from Marquinhos and set up Mbappe for the second goal.
Ole Gunnar Solskjaer's men will now head to the Parc des Princes needing to score at least three goals to progress, without going to extra time.
United played well in the first half but lost both Anthony Martial and Jesse Lingard to injury at half time and without two of the men integral for their turnaround they struggled in the second half. They are muscle injuries so we will have to wait a couple of days'. "To tell the truth, I don't realise it yet", Kimpembe said after scoring in front of the travelling PSG fans.
Twenty years after winning the Champions League as a United player, this was Solskjaer's first taste of the competition in management having only previously coached Molde in his native Norway and Cardiff before being hired by United. "You can see that we've not played games at this level for a while".
The home side never recovered their composure as PSG produced a stunning second-half display to all but book their place in the last eight despite David de Gea's best efforts in the United goal. We're going to continue.
The Red Devils moved into the top four for the first time this season after a 3-0 win against Fulham at Craven Cottage on Saturday.