The Leverkusen goalkeeper seemed to have taken care of Rogic's long-distance shot before inexplicably spilling the ball to the arriving Tomi Juric, who gleefully tapped home.
The match in Sochi will be the sixth time that the two nations have faced one another, but while Germany won the first three, Australia have recorded a win and a draw in the last two contests.
"If we can play the style that we know, we can most definitely beat them".
Along with Germany and Australia, Group B includes Chile and Cameroon, which played their match on Sunday.
"One thing we won't underestimate is their ability to play the kind of football they've been renowned for".
"It's a loss and the loss falls on me, it's my responsibility".
With virtually a second-string squad at his disposal, the fact that Germany manager Joachim Low still had a few selection dilemmas spoke volumes of the strength at the disposal of Die Mannschaft. Inevitably the focus on Germany has centered on its callow squad, containing only three world champions from 2014 while numerous established stars have been given a break.
Germany's rawness wasn't obvious at all early in the game when a goal was created after only five minutes.More news: New Zealand try new black magic to end US America's Cup spell
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Australia barely escaped their own half in the opening 30 minutes, but they eventually started to build some momentum.
An equisite free kick by Aaron Mooy offered a great chance of the half but the Socceroos failed to capitalise as Trent Sainsbury broke free of the defence but meekly nodded the ball wide (35').
It was not to last.
Massimo Luongo then coughed up a penalty with a clumsy tackle from behind brought Goretzka down inside the box and Draxler stepped up and converted, sending Ryan the wrong way.
It was extended further three minutes into the second half.
With the Germans screaming for handball, the decision to give the goal was referred to the video assistant referee. After Tom Rogic had a shot blocked, Juric had his follow-up saved by Leno.
Australia kept up the pressure after that as substitutes James Troisi and Robbie Kruse, as well as Juric, all tested Leno in the final quarter.
Those moves paid off - Kimmich was effective midfield and Werner hit the post in the 75th minute - but the Germans still barely held onto the win.
"Being able to have the chance to get to that marker will be a massive honour in my career but, over time, I'd much prefer to take success in this competition because it's a massive competition", said Cahill, who vouched for Australia being revitalised under Postecoglou.