The France global and World Cup victor also became the youngest player - at 19 years and nine months - to score four goals in one game in the same amount of time.
The France worldwide scored four of the five goals in a wild 14-minute second half spell after Neymar had opened the scoring with a first half penalty and both sides had been reduced to 10 men before half-time. They are a great team - they showed that in the Champions League and in big matches.
Kylian Mbappe poses with the crowd and cameras during his goal spree for Paris St Germain.
Mbappe scooped the best young player award as France won the World Cup in the summer and is expected to become the first individual to retain the Golden Boy prize.
"I congratulate Kylian and I hope that he continues like this as football will thank him".
Neymar was equally complimentary in his post-match comments about Mbappe, saying: 'Kylian is a special guy, for whom I have a lot of affection.
'Kylian is one of them, he is a technical leader and the group respects him. Of course, I know my value, I know the pressure that exists, I know my responsibilities but we have many quality players who also have their responsibilities.
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Christine Blasey Ford, calling them "insulting". "There was no corroborating evidence he did so". All these angry people know that these people sitting in the Senate are making these decisions.
And on such form, it surely won't be long until he is considered for the prestigious best player in the world accolade.
On Mbappe, Tuchel was impressed by the teenager's quadruple but also suggested that he could and should have scored even more.
"I should have scored more goals, it's part of the steps I have to go to get to the top", he said. "However, he trained well and then worked tactically for the team here and sacrificed himself defensively". He took a shot from inside the box and scored the goal.
"I'm very satisfied because he has not lost confidence, he has been magnificent. With Neymar, the two of them were unsafe all the time". I don't forbid anything, ' he said.
The French world cup victor hit all four goals in a devastating spell just after half-time to add to Neymar's first-half penalty as PSG won a ninth league game in a row to break an 82-year old record.
'The Ballon d'Or? Why not?