Bayern enjoyed more possession than PSG and managed 31 shots – including 12 on target – as the German champion spent most of the night chasing after the game after dropping two goals after 28 minutes.
But despite a wave of attacks, PSG have held firm to condemn Hansi Flick to his first Champions League defeat as Bayern manager after 15 wins and a draw.
It was Mbappe who opened the scoring in two and a half minutes as he sent a shot through Manuel Neuer after Neymar carried the ball deep into Bayern’s half.
Marquinhos doubled the visitor’s lead by quietly finishing Neymar’s ball in the box before Eric Maxim Choupo-Moting’s header retreated for Bayern.
As the snow continued to pour in the second half, Bayern, who did not have injured striker Robert Lewandowski, continued to push for the equalizer.
It finally came as Thomas Muller guided in a Joshua Kimmich free-kick header for his 48th Champions League goal – the same tally as Andriy Shevchenko and Zlatan Ibrahimovic.
But the scores weren’t tied for a long time. Eight minutes later, Mbappe clinically finished a PSG break as he shot at the post near Neuer.
“We tried to hurt them with our strength and it worked tonight. But we are only at half time and in between we have a very important league game.”
The two teams meet in Paris next week in what promises to be another high-quality and breathtaking game.
With three away goals, PSG will be the favorites to advance to the semi-finals and increase their chances of winning the Champions League – something the club owners have been striving for for the past ten years.
For Bayern, who were denied by several saves from Keylor Navas, this was a difficult result to take given the manner of the defeat.
“We had a lot of chances to win this game, we are very bad at the moment … hopefully (next week) we have reduced our chances,” Alphonso Davies told BT Sport.
“ Excited but not excited ”
In Wednesday’s other Champions League game, Chelsea beat Porto 2-0 with goals from Mason Mount – who became the Blues’ youngest goalscorer in the Champions League in the round of 16 – and Ben Chilwell.
Chelsea suffered their first loss under Thomas Tuchel this weekend – a shock 5-2 loss to West Brom in the Premier League – but were rejuvenated in Sevilla, which serves as a neutral place for both legs of the tie in the middle of coronavirus travel restrictions.
Mount opened the scoring with an exquisite turn and finish on Jorginho’s pass and stayed in the lead as Edouard Mendy parried the efforts of Pepe and Moussa Marega on either side of the half.
Christian Pulisic hit the crossbar in the final 10 minutes before Chilwell increased Chelsea’s lead moments later when he took the ball from Jesus Corona and bypassed Agustin Marchesin to score in an open goal.
“We are happy but not too happy. We are excited but not excited. We are very aware that today we made a lot of good attacks and we scored two goals.”
The other two first legs of the quarter-finals kicked off on Tuesday with Real Madrid beating Liverpool 3-1 and Manchester City beating Borussia Dortmund 2-1.