The midfielder, making his 62nd senior international appearance, played just over an hour of the encounter before being replaced by Borussia Dortmund's Julian Brandt.
Die mannschaft will feel they should have won by a more handsome margin having boasted 72% possession and registered 18 shots on goal.
But they had to wait until the final ten minutes for the breakthrough in Muscat, which came from debutant Niclas Fullkrug.
Victory represents Gundogan and co.'s final match before the World Cup gets under way.
The 2014 champions' latest quest for success begins against Japan on Wednesday 23 November, with further Group E fixtures against Spain and Costa Rica to follow.