The 19-year-old found the net twice in four minutes to give his side control of the match in Kazan, with Antoine Griezmann opening the scoring from the spot and right back Benjamin Pavard lashing home a goal of the tournament contender.
Argentina had fought back through Angel Di Maria’s stunning strike at the end of the first half, with Gabriel Mercado diverting a Lionel Messi strike past Hugo Lloris to give La Albiceleste the lead after 48 minutes.
From there, though, France turned on the style - with Mbappe slotting two impressive strikes past Franco Armani - to blow away Argentina. A late header from Sergio Aguero gave the South Americans hope of a stoppage time comeback, but they will now head home after a tumultuous time at this World Cup.
France, on the other hand, announced themselves as challengers and move on to the quarter-finals where they will face either Uruguay or Portugal, who play on Saturday night.
TALKING POINT - This was the game France finally came to life at this World Cup
Until now, France had struggled to find their groove, particularly in the attacking third. But this showed that they can raise their game, illustrated by the three goals they scored in just 11 second-half minutes. Griezmann and Mbappe were the main men, with Paul Pogba also finding top form in the centre of the pitch. This was a statement of intent from Les Bleus who have now finally flexed their muscle at this World Cup.
France's forward Antoine Griezmann (L) vies with Argentina's forward Lionel Messi during the Russia 2018 World Cup round of 16 football match between France and Argentina at the Kazan Arena in Kazan on June 30, 2018.
Image credit: Getty Images
MAN OF THE MATCH - Kylian Mbappe (France)
This was a coming of age moment for the 19-year-old. Of course, a lot had already been said about the talent of the PSG forward, but this was the game where he truly announced himself as a global superstar. His lightning pace won the penalty from which Griezmann opened the scoring, and Mbappe later bagged a brace of his own. Argentina couldn’t handle him and on this basis they won’t be the last side to struggle in such a way at this tournament.
France: Lloris 5, Pavard 8, Varane 6, Umtiti 6, Hernandez 7, Kante 6, Pogba 8, Mbappe 9, Griezmann 8, Matuidi 6, Giroud 6. Subs: Tolisso 5, Fekir, Thauvin.
Argentina: Armani 5, Mercado 6, Otamendi 5, Rojo 4, Tagliafico 5, Enzo 5, Perez 6, Mascherano 6, Banega 5, Pavon 7, Messi 6, Di Maria 8. Subs: Meza 5, Fazio 5, Aguero 6.
9’ OFF THE CROSSBAR! So close to an opening goal for France. Griezmann whips a wicked free-kick from the edge of the box, smashing his effort against the Argentina crossbar!
11’ PENALTY KICK TO FRANCE! Rojo makes a clumsy challenge on Mbappe inside the box and the referee points to the spot.
Ángel Di María celebrates
Image credit: Getty Images
13’ GOAL! France 1-0 Argentina: Griezmann steps up to the mark and sends Armani the wrong way with his conversion. It was a cool penalty kick by the Atletico Madrid forward, although the goalkeeper seemed to dive quite early.
41’ GOAL! France 1-1 Argentina: WHAT A GOAL! Out of nowhere, Di Maria has smashed home an equaliser for Argentina! He had time 25 yards out and lashed home a left-footed finish past Lloris. Sensational! One of the goals of the tournament.
48’ GOAL! France 1-2 Argentina: Argentina have taken the lead! Messi collected a free-kick at the back post, turns and gets the shot away. Mercado gets a slight touch on the strike to divert it past Lloris, who was wrong-footed.
57’ GOAL! France 2-2 Argentina: ANOTHER INCREDIBLE GOAL! Sensational. Matuidi's cross from the left bounces all the way over to Pavard, who was running on to it from the right side and he smashes a strike into the top corner of the Argentine net!
64’ GOAL! France 3-2 Argentina: France are back ahead and it's Mbappe, their star man, who has restored their lead! The ball was bouncing around in the box, Mbappe managed to free up the space for the shot on his left foot and squeezes a shot through Armani.
69’ GOAL! France 4-2 Argentina: He's got another! France came forward on the counter, Giroud poked the ball through for Mbappe, who made no mistake in finishing past Armani. France have a two-goal lead and they have taken a grip of this game.
85’ MESSI WAS THROUGH! Just for a moment it looked like Messi was going to make this interesting. He knocked the ball past the French defenders, he was through... but he scuffed his shot!
France's Benjamin Pavard scores their second goal
Image credit: Reuters
93’ GOAL! France 4-3 Argentina: Hold on... is there one final push from Argentina? Messi finds Aguero with a cross from deep and the Manchester City striker heads home from about 10 yards out. We're going to have a grandstand finish here!
At 30.2 yards, Angel Di Maria's goal was the longest range goal scored at the 2018 World Cup so far.
Kylian Mbappe became the second youngest player to score at least two goals in a World Cup game after Pele against Sweden in 1958.