Buoyed by their favourites tag pre-match, France were prepared to show their mental strength as they look to add another world title to their 1998 triumph on home soil.
Cannoning the crossbar from an Antoine Griezmann free-kick saw Les Blues a flying start inside the opening 10 minutes.
Argentina seemed to struggle early on and a 70-metre solo run from Kylian Mbappe brought nerves, more so after earning the French a penalty after a collision with Marcos Rojo.
Griezmann went one better from his earlier free-kick and sent Franco Armani the wrong way from 12-yards before slotting down the middle after 13 minutes, 1-0.
Mbappe continued being a nuisance with his runs to the box, earning a free-kick on the edge of the box following a delightful long ball from Paul Pogba.
Pogba aimed to tuck away the resulting set-piece but was let down with a horror execution that flicked all the way to the stands of the back arena.
La Albiceleste were level seven minutes to halftime with a stunning long-range drive from Angel Di Maria, beating Hugo Lloris hands down.
The first change from the dugout came from Argentina as Federico Fazio replaced an ineffective Marcos Rojo at the start of the second half.
The goal inspired them to go ahead two minutes after halftime when a shot from Messi inside the box found its way past Lloris courtesy of Gabriel Mercado's flick.
The French were nearly level when a poor back pass from Fazio almost brought in Griezmann to poke home but forward failed to hit the target.
After playing every single World Cup clash thus far, Benjamin Pavard produced one of the moments of the tournament so far with a sublime first-time volley the left on 58 minutes to make it 2-2.
Les Blues then went ahead through the boot of Mbappe, who showed skill and composure to slot home a neat finish on 64 minutes for his second of the campaign.
The two-time world champions threw all their cards in attack with the introduction of Sergio Aguero.
However, it was France with the next chance and they made it count as Mbappe ran out wide to complete his brace following a swift counterattack.
In added time, Argentina pulled one back through the head of Aguero but there was to be no major come back as the French advanced to the last eight for the successive tournament.
France XI: Lloris , Pavard, Varane, Umtiti, Hernandez, Kanté, Pogba, Mbappé, Griezmann, Matuidi, Giroud.
Argentina XI: Armani, Mercado, Tagliafico, Mascherano, Rojo, Otamendi, Banega, Di Maria, Perez, Pavon, Messi.