Germany crushed Greece 4-2 to reach the Euro 2012 semi-finals, surviving a scare against the surprise quarter-finalists before putting them to the sword with second-half goals from Sami Khedira, Miroslav Klose and Marco Reus.
Joachim Loew's team were made to wait 39 minutes to break down a dogged Greek side when Philipp Lahm's swerving effort put them in front but they were stunned 10 minutes after halftime when Giorgos Samaras levelled on the break.
However, Khedira's rasping volley and a header from Klose, his 64th goal for his country, eased Germany's nerves and Reus added a fourth as the Germans set up a semi-final against England or Italy.
Greece grabbed a late consolation through a penalty from Dimitris Salpingidis.
Germany, who had never lost to Greece in eight previous meetings, were much-changed from the side that beat Denmark in their final group game, with Mario Gomez, Lukas Podolski and Thomas Mueller dropped to the bench.
Expecting gritty Greece to pack their defence, coach Joachim Loew opted for veteran Klose up front with pace and width supplied by Reus and Andre Schuerrle.
Aggressive from the start, Germany looked determined not to get bogged down on a pitch made heavy by two days of rain and they set about creating chances.
Schuerrle put the ball in the net after less than five minutes, prodding it in after Greece keeper Michalis Sifakis spilled Sami Khedira's shot on the greasy turf but a linesman's flag curtailed the celebrations.
Greece, with defensive midfielder Grigoris Makos replacing suspended skipper Giorgos Karagounis, dug in but it was one-way traffic as Khedira and Reus wasted good chances.
Coach Loew was visibly angry at his side's profligacy but the Germans remained patient and were rewarded after 39 minutes when Lahm produced an unstoppable finish that had watching German Chancellor Angela Merkel leaping out of her seat.
The ball was worked to him 25 metres from goal on the left and there was only one thing on his mind as took a few paces forward before unleashing a right-foot shot that swerved past the desperate dive of Sifakis.
It seemed the only danger to Germany was an occasional lapse in concentration and they were punished severely 10 minutes after the break when they were caught short at the back as Dimitris Salpingidis galloped down the right and slid in a pinpoint cross that was converted by Giorgos Samaras.
The equaliser was met with a sense of disbelief in the stadium, apart from a clump of 2,000 or so joyous Greek fans behind the goal.
Germany quickly cleared their heads and were back in front six minutes later when Boateng's cross was met with a stunning volley from Khedira before Klose climbed high to head in Mesut Osil's free kick.
With 2008 runners-up Germany on cruise control, Reus slammed in the fourth as their fans began to dream of a fourth European title that looks well within their grasp.