Neither coach made a change at the break, but France came out on the front foot - and they broke through when, after a VAR review, referee Andres Cunha pointed to the spot for a penalty.
The first decision overturned in a competitive fixture since Video Assistant Referees became part of the Laws of the Game proved a controversial one, with Josh Ridson adjudged to have fouled Antoine Griezmann after the referee initially waved play on.
It was a rare moment of fluency from the French, however, with the much vaunted attack of Griezmann, Kylian Mbappe and Ousmane Dembele unable to create opportunities when pace alone was not enough to get past the wall of Australian defenders.
Australia's midfielder Mile Jedinak (second left) is congratulated after scoring from the penalty spot during their Russian Federation 2018 World Cup Group C match against France at the Kazan Arena in Kazan on June 16, 2018.
France are hoping to join tournament favourites Brazil, Germany and Spain in the latter stages as they look to make amends for losing the Euro 2016 final to Portugal.
Paul Pogba later scored the winning goal in the 81st minute, and goal-line technology was used to confirm the ball had crossed the line after bouncing down off the crossbar. They will look to end their duck of not winning an worldwide trophy since 2000 when they reached the final of UEFA Euro 2016 at their own home soil.
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Les Bleus had started the game in ominous fashion, carving out three chances in the opening six minutes.
Australia weathered that early storm, though, and came agonisingly close to taking the lead after 17 minutes.
However midway through the first half, Australia started fighting back, with Sainsbury going close to scoring after a ideal free kick from Aaron Mooy.
France's early verve was sorely lacking for the remainder of the half, with Australia able to keep their more illustrious opponents comfortably at arm's length before the interval. But it would go to VAR and with the referee seeing some contact between the two players.
Australia bounced back superbly from that setback, though, and were level just four minutes later.
Australia were awarded a penalty of their own on hour mark when Samuel Umtiti handled in the box.