The Atletico Madrid star wrote his name into the history books after he went down under a tackle from Josh Risdon in the penalty box in the second half of the Group C fixture, AFP reported.
Referee Andres Cunha from Uruguay did not initially award a spot-kick but after viewing the VAR footage, ruled it was a penalty and Griezmann coolly slotted past Socceroos' goalkeeper Mathew Ryan.
"It's a good job there was video in this case," Griezmann told BeIN Sport TV.
"I think it was a penalty, he caught me on the left foot. Just after I got up, it was hurting a bit. That's not simulation."
But French celebrations were short-lived, Australia captain Mile Jedinak levelling only four minutes later after a clear hand ball by Barcelona defender Samuel Umtiti.
Didier Deschamps' men were frustrated throughout by a gutsy Australian defensive display and French pride was only restored in the 81st minute.
Chelsea striker Olivier Giroud, still wearing a bandage around a recent head injury, had replaced Griezmann only minutes earlier and played a one-two with Paul Pogba on the edge of the area.
The Manchester United midfielder's shot took a deflection off the boot of defender Aziz Behich before evading the outstretched hands of Ryan and bouncing over the line off the crossbar.
While Australia coach Bert van Marwijk admitted his disappointment at seeing VAR used against his side, he praised his players' efforts.
"I hoped that maybe one time there would be a very honest referee, and in that moment, that he wouldn't go to the video screen," the Dutchman said.
"I'm proud and disappointed, it was a very good performance. No one expected we could play like this against France. A lot of moments they didn't know what to do any more.
"That's a big compliment for us. If you lose because of a penalty you can talk about it... then (they scored) a lucky goal just before the end."