The first concrete chance of the game fell in the 11th minute when Franco Di Santo got his head to the ball from close range, but Thibaut Courtois read it well and punched it away.
The Belgian international's first start for the Blues wasn't to end in a clean sheet, however, as John Terry conceded a fortuitous penalty in the 20th minute.
Eljero Elia's spot kick was subsequently drilled low to the far right of the keeper to give the Germans the lead.
Worse was to come for Mourinho's men with just eight minutes to go in the first half as Clemens Fritz lobbed the ball forward to Ludovic Obraniak, who coolly headed it past Courtois.
Chelsea thought that they had halved the deficit at the end of the first half, but Mohamed Salah's unmarked effort was disallowed for offside.
Just before the hour the Blues were to be frustrated once again as a penalty appeal was turned down. Fritz appeared to catch the ball on his arm while attempting to block a Cesc Fabregas cross, but the referee waved play on.