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The 22-year-old struck a superb equaliser in the first half before notching a further two in the second half as he moved to third in PSG's all-time scoring charts.
There was a real swagger about Mbappe's performance and he was involved in a heated altercation with Alba in the second half.
The Barca defender told Mbappe "You're getting too big for yourself", which prompted Mbappe to tell him, in perfect Spanish, "In the streets I'll kill you".
Pitchside microphones picked up the exchange as Barca prepared to defend a PSG set-piece, with Gerard Pique also getting involved and getting the same reply from the Frenchman when he asked, "Who are you going to Kill?".
Moise Kean ended up holding Mbappe back and the situation was eventually diffused.
Jordi Alba to Mbappé: "You're getting to big for yourself."- M•A•J (@Ultra_Suristic) February 17, 2021
Mbappé to Jordi Alba: "In the streets I kill you
Alba to Piqué: "He's learning, the bugger is learning."
Piqué to Mbappé: "Who are you going to kill?"
Mbappé: "On streets I KILL you!" #BARPSGpic.twitter.com/o2Cyu8CDnH
Mbappe showing off his Spanish skills to Jordi Alba. pic.twitter.com/0Qxmp4EyoC- Mbappe FC (@KMbappeRM) February 17, 2021
Looooool Mbappe really told Alba: "In the streets I'd kill you" this guy is insane https://t.co/RhexCrDfSl- Mad. (@MadridEveryday) February 17, 2021
Alba: Mbappé, you're a bit conceited- EiF (@EiFSoccer) February 17, 2021
Mbappé: I would kill you if I saw you in the streets
What an elite mentality. Stone cold killer. https://t.co/Y5Dudnbzas
Pique's slaughtering of teammate Antoine Griezmann was also captured and heard clearly at the empty Camp Nou in the first half, when the scores were at 1-1.
"Let's have a long possession, for f**k's sake. F**king hell! Let's go. A f**king long possession!" shouted a returning Pique at his colleagues, according to Marca's translation.
Griezmann replied: "Calm, Geri, stop shouting." To which Pique responded: "F**king hell Grizzi, f**k's s...".
Griezmann: "F**k you."
Pique: "No, f**k you. We're suffering and it's been like this for five minutes." Griezmann: "Don't shout."
Griezmann's fellow French international Clement Lenglet tried to act as peacemaker between the pair, but it didn't quite work.
"Motherf***er, we're running like crazy," Pique shouted. Griezmann replied: "I'm running too."
Pique, playing in his first game since November, was given the runaround by Mbappe. He was terrorised by the former Monaco man and had to resort to tugging on his shirt to stop him from racing clear.
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