The 2008 finalists overcame first-half frustration against the Hellenic side, with Khedira, Klose and Reus adding to Lahm's brilliant first-half strike to progress
A first half which saw profligate finishing from the 2008 finalists, Philipp Lahm broke the deadlock with a fine long-range strike after 39 minutes. Greece secured a shock equalizer 10 minutes into the second half with Georgios Samaras tapping in a Dimitris Salpingidis cross.
Germany retook the lead after 61 minutes with a sumptous Sami Khedira volley from close-range, before Miroslav Klose headed a third seven minutes later. Marco Reus made it 4-1 with 15 minutes left before Salpingidis converted a penalty a minute before time as Germany secures a semifinal place for the fourth consecutive tournament.
Die Mannschaft began the game in typically efficient fashion, and were unlucky not to be ahead after just four minutes. A nervy Michalis Sifakis spilled a Khedira effort back into play, with tournament debutant Andre Schurrle firing in low under the goalkeeper before the goal was ruled out for offside.
Fernando Santos' men failed to offer attacking creativity in much of the early proceedings at the PGE Arena - a testament to their game-plan - with a lone shot from Grigoris Makos saved easily by Manuel Neuer. In contrast, at the other end, Marco Reus fired an effort wide on goal after a brilliant move from midfield.
Germany upped its tempo as Greece initiated a period of stability, and it almost paid dividends. Reus played an intricate one-two with Klose before spreading the ball out wide to Ozil. The Real Madrid midfielder could then only fire at Sifakis before the ball was hurriedly cleared by Papadapoulous.
Seconds later, the lively Reus spurned two glorious chances as Germany failed to impose on its dominance. Firstly, with Ozil pulling the strings on the flank, the 23-year-old swept the ball across goal which was agonisingly missed by an oustretched Klose before slicing a shot wide as Greece floundered.
With the Ethniki seemingly cornered by the Germans, the 2004 winners weren't without their own opportunities. A superb ball from stand-in captain Kostas Katsouranis carved open a suspect defense, as Sotiris Ninis forced Manuel Neuer into an awkward save, with the goalkeeper needing a second save to make sure.
Further efforts were subsequently wasted by Joachim Low's men towards the end of the first half. A Schurrle effort curled frustratingly wide, before Khedira's fierce effort was again blocked by the impressive Sifakis as a resilient Greek defense held sway.
Greece's luck would indeed run out five minutes before halftime. Lahm dribbled his way into position outside the area before unleashing a superb swerving strike which deceived Sifakis and nestled into the bottom corner to give die Mannschaft the lead. Schurrle failed with a chance to make it two before the interval, shooting inches wide of goal.
The Ethniki were noticeably improving as the game wore on, but were almost 2-0 down after a horror clearance from Sifakis found Schurrle who, instead of shooting, opted to thread a ball towards Klose with the move breaking down.
At the other end, Katsouranis picked out Samaras with a fine pass, as Greece moved into a two against two before substitute Theofanis Gekas failed to reciprocate a back-heeled pass.
Nevertheless, the Greeks weren't to be outdone. A quick-fire counterattacking move saw Dimitris Salpingidis race down the right before squaring a low cross towards Samaras, who positioned himself in front of Jerome Boateng and bundle the ball past Neuer to send the traveling Greek support into delirium.
The celebrations were short-lived, six minutes in fact as Germany emphatically recovered to take the lead just past the hour. A speculative cross from Boateng on the flank was spectacularly met with the foot of Khedira, whose volley rifled into the roof of Sifakis' goal.
The Greek resistance came to a halt after that setback, and Germany took full advantage. Ozil's inswinging delivery from the corner saw Klose rise highest to head home into an empty net after Sifakis opted to commit himself in clearing, as the Lazio forward claimed his 64th international goal.
On another typically German break, Klose latched onto Ozil's neat pass, before firing at Sifakis who blocked the ball to the feet of Reus, who powerfully fired into an empty net, securing the Germans' record-breaking 15th competitive win. Boateng was deemed to have handballed late on, with Salpingidis converting a penalty as Greece exited the tournament on a high.
Joachim Low's men progress to the semifinal where they will meet either England or Italy on Thursday at the National Stadium in Warsaw.