Captain Philipp Lahm opened the scoring with a fine swerving strike before Fernando Santos' men scored a shock equaliser through Georgios Samaras early into the second half.
Sami Khedira fired home a sumptuous volley to retake the lead, before Miroslav Klose and Marco Reus made it 4-1. Dimitris Salpingidis converted a penalty late on, which proved mere consolation as die Mannschaft progressed to the last four for the fourth tournament running.
|Germany 4-2 Greece
The 52 year old trainer, who oversaw Germany's record-breaking 15th consecutive competitive win waxed lyrical over his side, before remaining cautious over the identity of their semi-final opponents.
"It is an achievement of class by this team to have reached a semi-final for the fourth consecutive time. I think, we all can be proud of this team." Low told German broadcaster ZDF.
"This team [Greece] again had one chance and scored two goals. We missed out on scoring in the beginning. But we kept going and scored lately. It was important that we showed a reaction after [being pulled back to] 1-1.
"It was a day of changes. After three wins in a row, I had the feeling I had to change something and bring some fresh air into the team. It was the time to change something.
"Khedira is having an unbelievably good run. He trains well, he always wants to have the ball. His team-mates feel that and they trust him. Ozil played with absolute class. He made very good runs and he managed to give the right impulses for the team.
"[On next opponent] That is pretty hard to say. England are a lot disciplined in their play than in 2010, for example, and Italy is always a difficult opponent. It doesn't matter who [qualifies].
"England are much better than in 2010 with Roy Hodgson. In a short time he built up a very compact team. Now they play as a team. And now are good at counterattacks. Hodgson has coached the team very well.
"As for Italy, they are always great in the defence, you know that, and have developed their game in counter attacks as well. Both teams [England and Italy] will be very dangerous. All the teams in the semi-finals have an equal chance to win the title.
"All the teams are about the same level. Just little things can decide the games and thus you should not allow yourself make mistakes."
Germany play the winner of the fourth quarter-final between England or Italy in Thursday's semi-final. Kick-off at the National Stadium in Warsaw is at 20:45CET.