Germany made history Sunday as it completed a perfect run through the "Group of Death" to win all three Euro group games for the first time ever.

Lars Bender scored the match-winner in the 80th minute with his first goal for Germany, and Lukas Podolski celebrated his 100th international appearance with his 44th goal in a 2-1 win over Denmark at Arena Lviv in Euro 2012.

"It was a special occasion to mark my 100th cap with a goal," Podolski said. "But the most important thing is that we are through to the knockout stage."

Germany defeated Portugal, the Netherlands and Denmark to win Group B, and the three-time Euro winners will play Greece in the quarterfinals Friday. Denmark was eliminated.

Portugal also advanced from Group B with a 2-1 win Sunday over the Netherlands to finish second. Portugal will play the Czech Republic on Thursday.

Although the Germans did not seal their place in the quarterfinals until late, Joachim Loew's side was in control for the majority of the fixture against the Danes.

Thomas Muller nearly gave Germany the lead inside 6 minutes, but his shot from close range was denied by a foot save from Denmark goalie Stephan Andersen.

Muller turned provider inside 20 minutes as Germany opened the scoring. He was able to flick on a cross from Mario Gomez on the near side of the 6-yard area, and Podolski hammered the ball past Andersen from close range.

The 27-year-old Podolski, who made his international debut for Germany in '04, is the youngest European player ever to reach 100 caps.

Denmark did not allow Germany to celebrate long, however. Off a corner kick in the 24th minute, Nicklas Bendtner headed the ball into the middle for Michael Krohn-Deli to head past Germany goalkeeper Manuel Neuer.

Sami Khedira and Gomez both had chances to send Germany into halftime with the lead, but failed to convert.

Denmark did not create many chances, but it was dangerous when it did test the German goal. Jakob Poulsen just missed the go-ahead goal in the 51st when he drilled a shot just inches wide of the left post.

Podolski gave way to Andre Schurrle in the second half, and the substitute had the first good chance for Germany after the break. Schurrle sent a low shot to the right side, but Andersen dove to palm the ball away from the corner.

Bendtner had a rare chance in the 76th when he fought off German center back Holger Badstuber to loop a header at Neuer, but Germany put the game away just minutes later.

With Portugal ahead in its match against the Netherlands, Denmark needed a win to advance and Germany pounced on a quick counter. Mesut Ozil played the final pass, just in front of teammate Miroslav Klose to Bender, who made a run from his place at right back to slot home the winner to the bottom left.

Making his first start of the tournament in place of suspended Jerome Boateng, Bender was strong in just his ninth international match, and capped the outing with a memorable match-winner.

"I will remember this day for a very long time," Bender said.

Daniel Agger headed over the bar in the 84th as Denmark created one chance in the closing minutes and Germany easily held on through stoppage time to secure its first perfect run in nine Euro finals since group play started in 1980.

"Right now I am very disappointed," Krohn-Dehli said, "just like the rest of the team."