PSG beat Nantes 4-2 on Saturday night at the Parc des Princes with Mbappe getting on the scoresheet in the last minute.
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He became the club's all-time highest goalscorer in the process, taking his total tally to 201 and surpassing Edinson Cavani as a result.
But despite the achievement, Mbappe still took the time at full-time to seek out opponent Ignatius Ganago, who lost his daughter two weeks ago.
In a mark of respect, the France international swapped shirts with the 24-year-old, who also scored during the contest.
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His daughter, Chloe, tragically lost her life at the age of five last month after suffering from an illness.
Nantes wrote on Twitter: "FC Nantes is in mourning. It is with deep sadness that the Football Club of Nantes has learned of the death of our striker's daughter, Ignatius Ganago.
"We think a lot of you Gana. The Club is with you through this terrible ordeal."
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According to Espoirs De Foot, Mbappe and Ganago exchanged shirts in the tunnel after the match and warmly embraced.
PSG extended their lead at the top of Ligue 1 by 11 points with their victory over Nantes on Saturday.
Lionel Messi opened the scoring early in the contest before an own goal from Jaouen Hadjam.
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The highly-rated Ludovic Blas managed to claw one back after a fine strike from an incredibly tight angle left Gianluigi Donnarumma dumbfounded.
And Ganago had equalised for the away side before half-time but PSG ramped it up after the break.
Danilo Pereira scored to give the French champions the lead before Mbappe's 92nd-minute strike saw him write history at the Parc des Princes.
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The 24-year-old's goal was his 201st for the club in just his 247th appearance having joined from Monaco in 2017, initially on loan.
Speaking after the match, the World Cup winner said: "In the last five minutes, I wasn't putting any pressure on myself, I knew I would beat it and I didn't want to force it.
"It's great that the goal came at the end. Playing here is a privilege, I've improved as a player, I've changed a lot.
"Playing at PSG is special for me. If you told me I would score with the captain's armband on to break the record, I wouldn't have believed it."