Mbappe, 19, was in a devastating form in the heavyweight clash, scoring two second-half goals in the 64th and the 68th minute respectively.
Not just that, the Paris Saint-Germain forward's surging 70-yard burst also led to the opening goal after 13 minutes, when Antoine Griezmann slotted home a penalty spot after Mbappe had been hauled down by Marcos Rojo in the area.
However, Argentina turned the game around thanks to Angel Di Maria's stunning long-range strike in the 41st minute.
While both the sides were 1-1 at halftime, Gabriel Mercado got France a lead in the 48th minute.
However, Benjamin Pavard scored a stunning equaliser in the 57th minute.
What happened next was not expected by Lionel Messi fans as Mbappe took the centre stage with a quick-fire brace and scored two goals in quick succession.
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Messi, whose international career future will be a burning question in the aftermath of the defeat, did set up a late header for Sergio Aguero in extra time, but it was not enough to save Argentina from slipping out of this year's tournament.
While Argentina were defeated by former champions Germany in the 2014 FIFA World Cup, fans of Lionel Messi had high hopes from the star footballer from this edition.
However, Messi has only managed to get one goal in the entire tournament - that came against Nigeria in their final group stage encounter.
France will next take on either Uruguay or Portugal in the quarter-final.