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The hosts could have surged ahead after 20 minutes had Ilkay Gundogan's right-footed volley not come off the inside of the Kazakhstan post.
Five minutes later Ozil floated a delivery inside the Kazakhstan penalty box that Gundogan turned in to make it 3-0.
Heinrich Schmidtgal pulled one back for the visitors in the opening minutes of the second half, but it failed to instigate any fightback.
Instead, it could have finished 5-1 to Germany had Thomas Muller not been denied twice in a minute by the frame of the Kazakhstan goal late in the half.
Valeri Korobkin also was denied by the post for the visitors with 11 minutes of normal time left on the clock, before Reus scored his second goal of the evening at Grundig-Stadion on 90 minutes to wrap up the win for Germany.