Lars Stindl scored his first Germany goal after just five minutes.
Captain Julian Draxler confidently tucked away his penalty to restore the advantage.
Leon Goretzka was a key figure in the 90 minutes and deservedly got on the scoresheet.
Germany got their Confed Cup campaign off to a winning start after seeing off a spirited Australia 3-2 in Sochi on Monday evening.
A first strike in their nations' colours for Lars Stindl and Leon Goretzka either side of a penalty from Julian Draxler were enough for Joachim Löw’s side, who twice watched their opponents from Down Under pull within a goal thanks to Tom Rogic and then Tomi Juric.
The game was the first of three in the Group for an experimental Die Mannschaft squad, who will also meet Chile and Cameroon over the course of this week.
It took the 2014 World Champions just five minutes to open scoring, as Borussia Mönchengladbach’s Stindl swept home from eight yards after a cross from Julian Brandt.
Germany continued to dominate thereafter, with Hoffenheim’s Sandro Wagner wasting a close-range header and a 1-on-1 before Brandt forced a fine save from Mathew Ryan with a drive from distance.
The Socceroos’ almost forced a shock equaliser when Trent Sainsbury misjudged a header from a free kick and those in yellow did draw level moments later when Rogic fired under Bernd Leno from 18 yards at the second attempt after his first wayward effort came back to his feet.
Parity was short-lived, however, as captain Draxler calmly stepped up from the spot to restore the lead on the brink of half time after Goretzka was hacked down in the area.
Schalke’s Goretzka extended the advantage from close range after the break following a pass from Joshua Kimmich, but Australia continued to make a game of it by pulling another one back shortly after.
Goalkeeper Leno failed to hold onto a free kick, leaving Juric to tap home into an empty net - a goal confirmed only after the Video Assistant Referee (being used in the tournament for the first time) clarified there had been no handball by Juric from the initial shot.
RB Leipzig’s Timo Werner - the highest scoring German from last season’s Bundesliga - was introduced midway through the second period, and hit the post in Germany’s best chance in the remaining minutes.