Germany flatten Greece 4-2 to make Euro semis
German captain Philipp Lahm turned his team's domination into a lead on 39 minutes with a swerving shot from distance.
Greece pulled it back to 1-1 against the run of play in the 55th minute, when Georgios Samaras finished a rare counterattack by hammering the ball into net.
Midfielder Sami Khedira halted the Greek celebrations just six minutes later, volleying Jerome Boateng's cross under the bar.
Miroslav Klose, replacing the German top scorer Mario Gomez in the starting eleven, headed a third on 68 minutes, nodding into an empty net from a Mesut Ozil free kick.
German midfielder Marco Reus sealed it on 74 minutes by powering in under the crossbar after Michalis Sifakis had saved Klose's shot.
Dimitris Salpigidis scored a consolation penalty for Greece a minute from time after Boateng handled in the penalty area.
Germany play England or Italy - who face off on Sunday - in Thursday's semifinal in Warsaw.
Germany were the only of the competition's 16 teams to emerge from the group stage with three wins, beating Portugal 1-0, the Netherlands 2-1 and Denmark 2-1.