Goals from Davor Suker, Goran Vlaovic and Robert Jarni gave Croatia victory in their quarter-final clash against Germany in Lyon on Saturday.
An 84th minute goal from Suker beat the keeper at the near post and followed a superb 20-yard strike from Vlaovic and a stern shot from Jarni on the stroke of half-time.
Earlier German defender Christian Woern was given the red card - leaving his side one man down. Woern was sent-off after an untidy tackle from behind on Davor Suker.
Germany had undoubtedly had the better of the first-half with only a superb double save by Croatian keeper, Drazen Ladic, keeping his side in the game.
Oliver Bierhoff headed down a good cross by Joerg Heinrich in the 29th minute - only for it to be parried away twice by Ladic once with his hands and then with his foot.
Earlier German wing back Joerg Heinrich was shown a yellow card in the 18th minute for an untidy tackle on Croatian defender Robert Jarni.
The match was tough but the game had little of the over-aggressive tackling which dominated the sides' last clash in the quarter-finals of the 1996 European championship when the Germans won 2-1.
The Croats started well after the break, playing the ball around with confidence. After two minutes Zvonimir Boban tapped the ball just over the bar after a pass into the box from the left from Jarni.
In the 53rd minute the Germans went close to equalising when Bierhoff struck a close-range shot after a corner from Tarnat, but Ladic just managed to get down to stop the ball going over the line.
Bierhoff thought the shot had gone over the line and appealed to the linesman but television replays showed clearly that Ladic had kept it out.
Croatia should have gone 2-0 up after 12 minutes of the half when Suker had a chance to score after a cross from the right from Stanic. But the striker hit his shot just wide of the right-hand post.
The Germans worked hard to try to get back into the match. But it was the Croats who were creating the chances.
And when they came - the finishing was deadly.
Vlaovic effectively finished off the Germans with a superb shot from just outside of the box which flew into the left-hand corner of the net - leaving Koepke helpless.
But minutes later Suker dealt the final blow in 85th, rifling the ball home from six metres for a 3-0 lead.
Teams:
Germany: Andy Koepke; Lothar Matthaeus; Juergen Kohler; Christian Woerns; Joerg Heinrich; Dietmar Hamann; Jens Jeremies; Michael Tarnat; Thomas Haessler; Juergen Klinsmann (captain); Oliver Bierhoff.
Croatia: Drazen Ladic; Igor Stimac; Slaven Bilic; Dario Simic; Robert Jarni; Zvonimir Soldo; Aljosa Asanovic; Zvonimir Boban (captain); Mario Stanic; Davor Suker; Goran Vlaovic.
Referee: Rune Pedersen (Norway)
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