Mbappe, who scored a hat-trick against Barcelona last month as they ran riot in a 4-1 victory at Camp Nou, slotted home the opening goal from the spot in the return leg at the Parc des Princes as a 1-1 draw on the night was enough for PSG to go through.
The penalty was given by referee Anthony Taylor after a VAR review, with Mauro Icardi deemed to have been tripped in the box.
Messi, who hit back with an absolute thunderbolt to level the scoreline and then missed a penalty, became the youngest player in history to score 25 when he was 22 years 86 days old.
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