England started the stronger side, but fell behind when Davie Selke struck the opener on 35 minutes for the Germans at Stadion Miejski Tychy.
Aidy Boothroyd's side hit back courtesy of efforts from Demarai Gray on 41 minutes and Tammy Abraham nine minutes later.
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But Felix Platte levelled with a header on 70 minutes as England were forced to battle to extend the match to extra-time and potentially penalties.
Platte appeared to have struck the winning goal on 79 minutes, but he was deemed to be offside which looked a marginal call from a linesman.
The winners will play Spain or Italy in the final with the second semi-final due to begin at 8pm.
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