France led the pack through Antoine Griezmann's penalty after only 13 minutes. Mbappé was the maker, tearing through the France defence before being bundled over by Marcos Rojo. Griezmann sat tight for Franco Armani to jump to one side before opening the spot-kick down the centre.
Argentina equalised just before half-time with Ángel Di María twisting home a lavish exertion from separate.
What's more, three minutes after the break they had the lead, with Lionel Messi's shot diverted past Hugo Lloris in the France goal by Gabriel Mercado.
The lead kept going under 10 minutes on account of another sublime exertion from distance. This time the ball dropped to the France appropriate back Benjamin Pavard, who roared a half-volley past Armani to make it 2-2.
Mbappé at that point conveyed the unequivocal blows. Initially, on 64 minutes, the 19-year-old wriggled space in the region and lashed a shot low past Armani, however, the goalkeeper may have improved the situation.
After five minutes he put Olivier Giroud's go into the base corner to give France a 4-2 lead.
France maybe ought to have added to their count in the end stages, while Lionel Messi missed a half-chance for Argentina with five minutes to go. Sergio Agüero at that point gestured home Argentina's third profound into injury time yet it was short of what was expected.
Les Bleus will play the winners of Uruguay v Portugal in Nizhny Novgorod on Friday in the quarter-finals.
