Germany felt a bit of scare when Emre Can got himself dismissed early in the first half.
But despite being reduced to 10 men, the Mannschaft opened the scoring right after the re-start as Gundogan rippled the net from outside the box with an emphatic first-time effort.
The 28-year old Man City midfielder then doubled the damage before the hour-mark, with a sweeping finish which took a deflection.
And to top it off, Gundogan produced a diagonal pass from the halfway line for Timo Werner who buried the ball into the net with a surgical shot in the 70th minute.