Philipp Lahm gave Germany the lead in the 39th minute before Georgios Samaras equalized for Greece in the 55th. But Sami Khedira, Miroslav Klose and Marco Reus all scored to pull Germany clear. Dimitris Salpigidis scored a consolation penalty for Greece in the 89th after Jerome Boateng handled.
German Chancellor Angela Merkel made the trip for the match and stood to cheer every time her team scored.
The match was played amid the political backdrop between the countries. Germany has been a major contributor to economic bailouts for Greece and was instrumental in demanding unpopular spending cuts.
Germany dominated nearly the entire match, but the Greek defense held strong for much of the first half. Lahm finally put his team in front by controlling the ball with his chest and dribbling toward the middle before sending a long-distance shot into the corner off the hand of Greece goalkeeper Michalis Sifakis.
The Greeks looked better at the start of the second half, and even equalized when Samaras knocked the ball past Germany goalkeeper Manuel Neuer after a perfect cross from Salpigidis.
But after that, it was all Germany.
Khedira volleyed in a cross from Boateng in the 61st, and Klose headed in a free kick from Mesut Oezil in the 68th as Sifakis was late to punch the ball away.
Reus made it 4-1 in the 74th, volleying a shot in off the underside of the crossbar after Sifakis had saved from Klose.
Salpigidis scored from the penalty spot after Boateng handled.
Germany coach Joachim Loew dropped his three main forwards for the match, including leading striker Mario Gomez, but their replacements did just fine.
Klose, who has Polish heritage, constantly troubled the Greek defense and linked up well with Oezil and Andre Schuerrle.
Greece had one major change in its lineup, but it was because of suspension. Captain Giorgos Karagounis sat out the match after picking up a yellow card in the 1-0 win over Russia for diving.
Without him in the midfield, the Germans had little trouble controlling the play and creating chance after chance.