Germany produced a dominant display to sweep past a limited Greece side and set up a possible Euro 2012 semi-final with England.
Germany wasted a host of early chances before captain Philipp Lahm fired them ahead in spectacular fashion.
"Germany have won at a canter. There was complacency about changing the front three and it didn't work out for them at first. When Greece got back to 1-1, you feared for them but then there were quality goals from quality players. That put the game beyond doubt. Germany are good, but they are not brilliant."
Greece threatened a scare when Celtic striker Georgios Samaras levelled on the counter-attack, but Sami Khedira and Miroslav Klose soon responded.
Marco Reus thumped home a fourth before Dimitris Salpingidis netted a penalty.
Germany will now take on England or Italy in the last four in Warsaw next Thursday.
German coach Joachim Loew raised eyebrows before kick-off with his decision to rest his first-choice strike trio of Mario Gomez, Thomas Mueller and Lukas Podolski.
But his decision was vindicated as young replacements Reus and Andre Schurrle turned in energetic performances either side of the vastly experienced Klose, who saw an early strike ruled out for offside.
Reus in particular could have had a couple of goals in a first 45 minutes completely controlled by Loew's side, with the coach growing visibly frustrated as the half wore on and his team wasted a flurry of openings.
The breakthrough came just before the break when Bayern Munich full-back Lahm cut inside from his station on the left and thrashed a right-footed shot from 20 yards which bent wickedly past goalkeeper Michalis Sifakis and into the corner.
Greece coach Fernando Santos made two changes at the break as he attempted to offer some sort of attacking outlet and, despite the opening 10 minutes continuing the pattern of German ascendancy, Samaras then struck against the run of play.
Replacement Giorgos Fotakis released Salpingidis down the right, and he was able to pick out Samaras at the back post to slide in from close range.
If it was an examination of this Germany side's credentials, it was one they passed with ease as they responded by scoring three goals in 13 minutes.
First Khedira - playing in a far more advanced role than the one he fills for Real Madrid - showed fine technique to strike a volley into the roof of the net, before Klose took advantage of some poor goalkeeping by Sifakis to nod in a simple header from a free-kick.
It was Klose's 64th international goal and his 17th in a major tournament.
Who is Marco Reus?
- Born in Dortmund in May 1989
- Scored 21 goals in 37 games for Borussia Monchengladbach last season
- Earned a £15m move to hometown club Borussia Dortmund
- Scored his second international goal against Greece
Reus then grabbed the goal his performance deserved with an emphatic finish off the underside of the crossbar after Sifakis had smothered Klose's shot, before Salpingidis reduced the deficit from a penalty awarded for handball against Jerome Boateng.
It was a performance by Germany that made pre-match talk of Loew taking a gamble with his team selection look rather fanciful.
And for semi-final opponents Italy or England, there is also the knowledge that the trio of Podolski, Gomez and Mueller - with 79 international goals between them - will now be desperate to earn back their places in the starting XI.
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Live Text Commentary
Full Time The referee brings the game to a close.90:00 +1:26
Nikos Liberopoulos concedes a free kick for a foul on Jerome Boateng. Manuel Neuer takes the free kick.90:00 +1:20
Giannis Maniatis sends in a cross.90:00 +0:11
Foul by Giorgos Fotakis on Mario Gotze, free kick awarded. Direct free kick taken by Mario Gotze.88:40 Goal scored
Goal! - Dimitris Salpingidis - Germany 4 - 2 Greece Dimitris Salpingidis scores a placed penalty. Germany 4-2 Greece.87:41
Centre by Vassilis Torosidis. Jerome Boateng handles the ball and concedes a .87:15
Mario Gomez gives away a free kick for an unfair challenge on Socratis Papastathopoulos. Michail Sifakis takes the free kick.86:39
Mesut Ozil gives away a free kick for an unfair challenge on Dimitris Salpingidis. Free kick taken by Kyriakos Papadopoulos.85:22
Georgios Samaras produces a cross.84:44
Mesut Ozil takes a shot. Save by Michail Sifakis.82:07
Giorgos Fotakis takes a shot. Comfortable save by Manuel Neuer.81:03
Dimitris Salpingidis delivers the ball.80:31
Mario Gomez is flagged offside by the assistant referee. Michail Sifakis takes the indirect free kick.80:22
Mesut Ozil takes a shot. Save by Michail Sifakis.79:48
Unfair challenge on Sami Khedira by Giorgos Fotakis results in a free kick. Free kick taken by Bastian Schweinsteiger.78:54 Substitution
Substitution Mario Gotze on for Marco Reus.78:54 Substitution
Substitution Mario Gomez replaces Miroslav Klose.78:44
Georgios Samaras produces a right-footed shot from just outside the box that misses to the right of the net.76:38
Free kick awarded for an unfair challenge on Giorgos Fotakis by Mats Hummels. Giorgos Fotakis takes the free kick.74:50
Free kick taken by Bastian Schweinsteiger.
Booking Socratis Papastathopoulos is cautioned by the ref for unsporting behaviour.74:42
Unfair challenge on Mesut Ozil by Socratis Papastathopoulos results in a free kick.73:23 Goal scored
Goal! - Marco Reus - Germany 4 - 1 Greece Marco Reus fires in a goal from inside the penalty area to the top right corner of the goal. Germany 4-1 Greece.73:22
Miroslav Klose takes a shot. Save made by Michail Sifakis.72:49
Nikos Liberopoulos takes a shot.71:15
Inswinging corner taken by Mesut Ozil from the right by-line, Georgios Samaras makes a clearance.70:40 Substitution
Substitution Grigoris Makos leaves the field to be replaced by Nikos Liberopoulos.70:40
Shot from inside the six-yard box by Thomas Muller goes wide right of the target.68:47
Miroslav Klose takes a shot. Save by Michail Sifakis. Inswinging corner taken by Mesut Ozil. Mesut Ozil delivers the ball. Bastian Schweinsteiger takes a shot. Giannis Maniatis gets a block in. Marco Reus crosses the ball, clearance by Kyriakos Papadopoulos.67:17
Assist on the goal came from Mesut Ozil.67:17 Goal scored
Goal! - Miroslav Klose - Germany 3 - 1 Greece Miroslav Klose grabs a headed goal from inside the box. Germany 3-1 Greece.66:09
The ball is swung over by Mesut Ozil,66:09 Substitution
Substitution (Germany) makes a substitution, with Thomas Muller coming on for Andre Schurrle.66:09
Unfair challenge on Mesut Ozil by Socratis Papastathopoulos results in a free kick.64:56
Corner taken right-footed by Giorgos Fotakis from the right by-line, Headed effort on goal by Kyriakos Papadopoulos from just inside the box goes harmlessly over the goal.64:43
The ball is swung over by Giannis Maniatis, blocked by Holger Badstuber.63:47
Free kick awarded for an unfair challenge on Socratis Papastathopoulos by Bastian Schweinsteiger. Vassilis Torosidis takes the direct free kick.63:09
Miroslav Klose is ruled offside. Indirect free kick taken by Socratis Papastathopoulos.62:20
Effort on goal by Theofanis Gekas from just inside the penalty area goes over the target.60:44
Jerome Boateng provided the assist for the goal.60:44 Goal scored
Goal! - Sami Khedira - Germany 2 - 1 Greece Sami Khedira gets on the score sheet with a goal from deep inside the penalty box high into the middle of the goal. Germany 2-1 Greece.60:42
Jerome Boateng sends in a cross,59:19
The ball is delivered by Andre Schurrle.57:12
Miroslav Klose gives away a free kick for an unfair challenge on Dimitris Salpingidis. Free kick taken by Grigoris Makos.56:52
Marco Reus produces a cross.56:15
Short corner taken by Bastian Schweinsteiger from the left by-line.54:42
Assist by Dimitris Salpingidis.54:42 Goal scored
Goal! - Georgios Samaras - Germany 1 - 1 Greece Georgios Samaras finds the net with a goal from inside the six-yard box to the bottom left corner of the goal. Germany 1-1 Greece.54:40
The ball is sent over by Dimitris Salpingidis,53:53
The assistant referee flags for offside against Dimitris Salpingidis. Holger Badstuber takes the free kick.53:03
Inswinging corner taken by Mesut Ozil from the right by-line, Holger Badstuber produces a right-footed shot from inside the area that goes over the bar.49:46
The ball is sent over by Vassilis Torosidis. The offside flag is raised against Dimitris Salpingidis. Manuel Neuer restarts play with the free kick.49:33
Andre Schurrle is penalised for handball and concedes a free kick. Free kick taken by Giorgos Fotakis.48:34
Socratis Papastathopoulos concedes a free kick for a foul on Marco Reus. Mesut Ozil delivers the ball from the free kick left-footed from right wing.47:51
Corner taken by Marco Reus, clearance by Kyriakos Papadopoulos.47:43
Miroslav Klose produces a cross, Kyriakos Papadopoulos gets a block in.45:01
The game restarts for the second half.45:01 Substitution
Substitution Giorgos Tzavelas goes off and Giorgos Fotakis comes on.45:01 Substitution
Substitution (Greece) makes a substitution, with Theofanis Gekas coming on for Sotiris Ninis.45:00 +3:29 Half time
Half Time The players leave the pitch at half time.45:00 +2:05
Free kick awarded for a foul by Socratis Papastathopoulos on Miroslav Klose. Direct free kick taken by Sami Khedira.45:00 +1:28
Andre Schurrle has an effort at goal from outside the penalty box which goes wide left of the goal.45:00 +0:57
Centre by Andre Schurrle.44:33
Mesut Ozil produces a drilled left-footed shot from 25 yards. Giorgos Tzavelas gets a block in.44:13
Mesut Ozil takes a short corner.43:58
Andre Schurrle produces a right-footed shot from the edge of the box and misses to the right of the goal.42:07
The assistant referee flags for offside against Miroslav Klose. Michail Sifakis restarts play with the free kick.41:58
Marco Reus takes a shot. Kyriakos Papadopoulos gets a block in.38:22 Goal scored
Goal! - Philip Lahm - Germany 1 - 0 Greece Philip Lahm grabs a goal from outside the box to the bottom right corner of the goal. Germany 1-0 Greece.37:57
Shot from 20 yards from Andre Schurrle. Blocked by Kyriakos Papadopoulos.37:52
Jerome Boateng crosses the ball, Kyriakos Papadopoulos manages to make a clearance.36:32
Grigoris Makos fouled by Mesut Ozil, the ref awards a free kick. Free kick taken by Socratis Papastathopoulos.35:51
Andre Schurrle produces a drilled right-footed shot from 35 yards that went over the goal. Short corner taken by Mesut Ozil.35:29
Sami Khedira takes a shot. Save by Michail Sifakis.34:52
Sami Khedira sends in a cross.34:12
Outswinging corner taken by Mesut Ozil from the left by-line.34:07
The ball is delivered by Philip Lahm, blocked by Vassilis Torosidis.33:47
Jerome Boateng delivers the ball, clearance made by Giorgos Tzavelas.32:48
Effort from the edge of the box by Andre Schurrle goes wide of the right-hand upright.31:44
Sotiris Ninis takes a shot. Save by Manuel Neuer.26:56
Marco Reus challenges Socratis Papastathopoulos unfairly and gives away a free kick. Socratis Papastathopoulos restarts play with the free kick.25:26
Dimitris Salpingidis challenges Bastian Schweinsteiger unfairly and gives away a free kick. Direct free kick taken by Mats Hummels.24:47
Effort on goal by Marco Reus from deep inside the penalty area misses to the right of the target.23:58
The ball is sent over by Mesut Ozil, Marco Reus has an effort at goal from deep inside the area missing to the left of the target.23:41
Corner taken by Mesut Ozil from the right by-line, clearance by Georgios Samaras.23:27
Marco Reus takes a shot. Michail Sifakis makes a save.23:18
The ball is sent over by Mesut Ozil, clearance by Grigoris Makos.23:03
Short corner worked by Mesut Ozil.22:47
Mesut Ozil takes a shot. Save by Michail Sifakis.22:20
Sami Khedira delivers the ball, Kyriakos Papadopoulos makes a clearance.21:43
Centre by Philip Lahm, Socratis Papastathopoulos manages to make a clearance.18:05
The ball is swung over by Marco Reus, blocked by Giorgos Tzavelas.15:31
Jerome Boateng sends in a cross.14:02
Mats Hummels takes the direct free kick.14:02 Booking
Booking Georgios Samaras is cautioned.13:56
Bastian Schweinsteiger fouled by Georgios Samaras, the ref awards a free kick.12:42
Unfair challenge on Sami Khedira by Georgios Samaras results in a free kick. Free kick crossed by Mesut Ozil, Kostas Katsouranis manages to make a clearance.10:48
Effort from the edge of the box by Marco Reus goes wide of the left-hand post.9:01
The ball is swung over by Sami Khedira.7:04
Grigoris Makos takes a shot. Save by Manuel Neuer.5:55
Sami Khedira produces a right-footed effort from long distance that goes harmlessly over the bar.3:15
Sami Khedira takes a shot. Save by Michail Sifakis. The assistant referee flags for offside against Miroslav Klose. Michail Sifakis takes the free kick.1:37
The ball is crossed by Marco Reus, Vassilis Torosidis makes a clearance.0:00
The referee gets the game underway.
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