Lionel Messi and Julian Alvarez struck on either side of interval as Argentina booked quarter-final spot following a 2-1 victory against Australia in their last-16 match on Saturday.
Argentina will face the Netherlands in the quarter-final on Friday, who beat USA 3-1 earlier tonight.
The first goal came in the first half when Messi slotted home from just inside the area beyond the reach of goalkeeper Mat Ryan after 35 minutes of a scrappy period of play with the only shot on target in the game so far.
The goal from Messi, playing in the 1,000 match of his career, was his ninth World Cup goal and the third of the ongoing edition, making him the joint-top scorer.
Following resumption, in the 57th minute, Alvarez and Rodrigo De Paul teamed up to press Australia goalkeeper and the former capitalised by slotting into an empty net.
Australia came back into the match after Argentina midfielder Enzo Fernandez deflected a shot for an own goal in the 77th minute.
Later, a darting run from Aziz Behich almost yielded an equaliser, while substitute Lautaro Martinez missed two clean-cut chances for the Albiceleste.
In the end though, Argentina saw through the final nervy minutes, courtesy of goal-keeper Emiliano Martinez.