With Guerrero starting on the bench, the responsibility of scoring Peru's first World Cup goal since 1982 fell at the feet of Christian Cueva.
"In Didier Deschamps we have got a manager who was in the dressing room in 1998", Griezmann told reporters before the game.
Peru take on Denmark in the other Group C match at the Mordovia Arena in Saransk later on Saturday. The referee and assistant didn't immediately flag for a goal, though, and the players waited on the field to see what the decision would be. He was 10 months younger than Bruno Bellone, who played at the 1982 World Cup in Spain. I think we've let Australia slow down the game.
However, Griezmann has backed the 25-year-old to live up to expectations at the World Cup and produce match-winning performances as France aim to go all the way.
Although Australian captain Mile Jedinak levelled from the spot four minutes later following an intentional handball by by Samuel Umtiti, goalline technology was used in decisive fashion when Paul Pogba's deflected shot crept over the goalline in the 81st minute. Nobody expected us to play like that against France.
Australia coach Bert van Marwijk and his players have taken aim at the officials and the use of technology after their heart-breaking 2-1 loss to France.
But after 15 minutes of solid defending, Australia grew into the game and conjured up the best chance so far.
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Pogba, whose victor was aided by goal-line technology after his strike clipped a defender and bounced off the underside of the bar, told TF1: "It is the World Cup - there are no small teams".
"It's not taking risks - they are here because they have the quality to be here".
While Deschamps was giving nothing away on Friday, only three will start with Griezmann's form making him nearly certain to lead the line and the experienced Giroud perhaps the player to miss out.
There was also some fairly naive positional play from Australia's full-backs, which Van Marwijk will want to address before the next group games.
"I think there were a lot of moments they didn't know what to do any more. a lucky goal just before the end. we deserved a draw".
"But we have almost a week before meeting Peru, so we hope to rectify that".