The hot favourites totally dominated the first half against a Greek team who set out to defend from the start and Germany went ahead when captain Philipp Lahm  cut inside and crashed home a swerving long-range drive six minutes before the break.
Greece, the 2004 champions, stunned the Germans 10 minutes into the second half when Dimitris Salpingidis escaped down the right in a rare attack and sent over an inch-perfect cross for Giorgos Samaras to slide in and bundle the ball over the line.
Germany hit back six minutes later when Jerome Boateng crossed for Sami Khedira to slam in an unstoppable volley from 10 metres. A Miroslav Klose header in the 68th and a thumping Marco Reus shot six minutes later took them into a Warsaw semi-final against either England or Italy.
Greece gave their fans something to cheer with a late consolation goal from the penalty spot through Salpingidis after Boateng was harshly adjudged to have handled in the area.