Mario Gomez scored twice for Germany, taking his tally to three goals in two games and leaving the Dutch needing victory over Portugal in their last Group B match to have any chance of progressing.
They are also dependent on Germany beating Denmark. The Danes came back from 2-0 down against Portugal thanks to two close-range headers by Nicklas Bendtner, before substitute Silvestre Varela smashed in the 87th-minute winner.
Germany have six points from two games, Denmark and Portugal have three and the Netherlands none.
DUTCH FACE EXIT
Gomez fired the Germans into a 24th-minute lead after turning in the area and firing past keeper Maarten Stekelenburg following a superb Bastian Schweinsteiger pass.
The pair combined again 14 minutes later, with Gomez scoring from a narrow angle on the right before Robin Van Persie cut the deficit with a sweet right-foot shot 17 minutes from time for his team's first goal of the tournament.
Portugal went ahead in Lviv when defender Pepe lost his marker from a corner by Joao Moutinho and headed powerfully past Danish goalkeeper Stephan Andersen.
Portugal doubled their lead in the 36th minute when striker Helder Postiga got in front of defender Simon Kjaer and shot past Anderson from close range after a pass by Nani. But it looked initially like Portugal, beaten 1-0 by Germany in their opening match, had let the Danes off the hook.
Bendtner scored from almost on the goalline in the 41st minute after Michael Krohn-Dehli looped a header over keeper Rui Patricio, and he nodded powerfully home in the 80th minute. But three minutes after coming off the bench, Varela took full advantage when he was given time and space and scored from eight metres at the second attempt after fluffing his first shot.
"Their equaliser was unfair at that stage of the match. We could have won the game more comfortably and with less suffering," said Portugal coach Paolo Bento.
The Danes need to pick up at least a point against Germany in the final match on Sunday and hope other results go their way. "It's a horrible feeling to lose so close to the end ... the Portuguese were a bit luckier. Maybe they were a bit better," coach Morten Olsen told reporters.
Although Nani had an excellent game, making one goal and generally tormenting the Danish defence, Cristiano Ronaldo misfired in front of goal. The world's most expensive player missed two good scoring opportunities and under-performed in a big international yet again.
