The Manchester City midfielder struck both aspect of half time as his side cruised to a cushty 7th successive win below new coach Hansi Flick.
Having already secured qualification back in October, there was little at stake for a German facet who have hit shape because the European Championships with 31 desires of their last seven games.
Kai Havertz scored an fashionable opener for Germany on 15 mins, flicking in a cross from Jonas Hofmann with the out of doors of his left boot.
Despite having nearly eighty percent of ownership in the first half of hour, Germany had been starved of area and struggled to create clean chances earlier than the destroy.
They needed a penalty to double their lead on the stroke of half time, Gundogan changing from 12 yards after a foul on Florian Neuhaus inside the container.
Gundogan were given a cheap second purpose early inside the 2nd half while Armenia goalkeeper Stanislav Buchnev fumbled his smooth shot from outside the container.
The hosts pulled a intention lower back to raucous celebrations ten mins later, Henrikh Mkhitaryan scoring from the spot after Neuhaus added down David Terteyan.
But Germany remained in complete control, and Jonas Hofmann restored their three purpose lead simply five mins later with a smart end into the lowest nook.
