Germany set up a Euro 2012 semifinal with England or Italy after a 4-2 flattening of 2004 champions Greece on Friday.
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.
Nevertheless, Joachim Low fielded a bold lineup with four changes to the side that started the Denmark game, relegating the two scorers in that match - Lukas Podolski and Lars Bender - to the bench.
The Greeks, who escaped from Group A with a shock 1-0 win over Russia, put up a slightly bigger fight than most had expected, with Grigoris Makos doing a reasonable job of filling the void left by the suspended Giorgos Karagounis, but they inevitably folded as the German triangle of Khedira, Bastian Schweinsteiger and Ozil proved irresistible.
Greece saw the ball in their net as early as four minutes, but Andre Schurrle, Bayer Leverkusen's 21-year-old starlet, was adjudged to have been offside.
A long-range shot from Borussia Dortmund's Reus whizzed past the post after Khedira released him.
Germany then blew a series of opportunities, all created by Reus.
First Sifakis denied Ozil, then Klose was inches away from making contact with a ball from the left, and finally the 23-year-old himself pulled a powerful shot just wide.
Greece responded only after the half-hour mark, when a shot from range by Sotiris Ninis was saved by the German keeper Manuel Neuer.
Schurrle could have doubled the lead before the break with another long-range strike, which turned soared just past the post.
Seven minutes after the break Neuer was forced into action again, capturing the ball firmly as Samaras was about to rush one on one in the penalty area.
The Germans went on to make their superiority count as soon as Low replaced Schurrle with Bayern Munich regular Thomas Muller.
Relaxed, they started to convert their chances and the game was over by the 74th minute.
Germany: Manuel Neuer, Philipp Lahm, Mats Hummels, Holger Badstuber, Jerome Boateng, Bastian Schweinsteiger, Sami Khedira, Marco Reus (Mario Gotze ,79), Miroslav Klose (Mario Gomez , 79), Andre Schurrle (Thomas Muller, 67), Mesut Ozil.
Greece: Michalis Sifakis, Vasilis Torosidis, Georgios Tzavelas (Georgios Fotakis, 46), Kyriakos Papadopoulos, Sokratis Papastathopoulos, Kostas Katsouranis, Giannis Maniatis, Grigoris Makos (Nikos Liberopoulos, 71), Dimitris Salpigidis, Georgios Samaras, Sotiris Ninis (Theofanis Gekas, 46)
