Jorge Sampaoli's side beat Nigeria 2-1 in St. Petersburg thanks to a last-gasp winner from Marcus Rojo, a result that means they finish second in Group D.
Lionel Messi scored a brilliant opener on 14 minutes, but a Victor Moses penalty early in the second half saw Nigeria equalise.
A draw would have seen Argentina eliminated at the group stage for the first time since 2002 but Rojo’s winner means they finish a point above the Super Eagles and qualify for the knock-out phase.
Messi is now the third Argentina player to have scored in three different World Cup tournaments, alongside Diego Maradona and Gabriel Batistuta.
Sergio Aguero was a second-half substitute in that match.
Croatia top Group D after their 2-1 win over Iceland. Zlatko Dalic's side took maximum points from their three group matches and look like a side to be feared in the last 16.
In Group C, France and Denmark played out the first 0-0 draw of the tournament, a result that sees both sides progress to the last-16. Benjamin Mendy made his first appearance of the World Cup as a second-half substitute in the Luzhniki Stadium.
France top the group to set up a last-16 match against Argentina in Kazan on Saturday, while runners-up Denmark play Croatia.
Peru won their first World Cup match in 40 years after a 2-0 victory over Australia that sees them finish third in Group C.
Attention now turns to the other half of the draw, with four matches to look forward to on Wednesday.
Brazil face Serbia in a key game for Tite’s men. Gabriel Jesus, Fernandinho and Ederson will all be hoping to be involved, but Danilo remains sidelined with a thigh problem. Both Brazil and Serbia can top Group E, finish second or be eliminated from the tournament.
Switzerland, who are currently level with Brazil on four points and face the same scenario going into their final match, play Costa Rica, who are already out.
And in Group F, Ilkay Gundogan could start for Germany in their decisive game against South Korea.
Joachim Low's side must win by two or more goals or better Sweden's result to guarantee qualification and remain on course to become the first side to retain the World Cup since Brazil in 1962.
Mexico play Sweden in the other match in that group. Mexico know a point is enough to secure top spot - and even a defeat is enough to send them through, as long as Germany fail to beat South Korea. Sweden are guaranteed to qualify if they win or better Germany's result. If they beat Mexico and Germany fail to win, Sweden will top the group.
Confused? All will become clear this evening. It looks like another brilliant day of World Cup football ahead.
Australia 0-2 Peru
Denmark 0-0 France
Iceland 1-2 Croatia
Nigeria 1-2 Argentina
Serbia v Brazil (7pm, ITV)
Switzerland v Costa Rica (7pm, ITV4)
Mexico v Sweden (3pm, BBC Two)
South Korea v Germany (3pm, BBC One)