The youngster's well-taken brace put paid to a spirited Japanese challenge that only faded in the second half as the impressive Asians began to tire, but the Nadeshiko nevertheless emerged with huge credit from this closely-matched encounter.
On 21 minutes, the German No1 came to her side's rescue by tipping round the post a low shot from Aya Miyama that seemed destined for the bottom corner. It was a fantastic save, but Angerer somehow contrived to better it just seconds later when she leapt to her left to claw away another goal-bound effort from the Japan forward.
The weary-looking Germans, for their part, failed to create a single clear-cut opportunity of note in a first half that belonged completely to their unfancied Asian opponents.
However, Silvia Neid's team have a well-deserved reputation for being able to grind out results even when they are not at their best, and the introduction of three young substitutes early in the second half provided them with the spark to do just that.
Of all the replacements, the introduction of Kosovo-born Bajramaj undoubtedly made the biggest impact, with the talented youngster firing Germany in front on 69 minutes from an acute angle after Kerstin Garefrekes' initial header had been parried clear.
Then, with the clock ticking down and Japan searching frantically for an equaliser, Bajramaj sealed Germany's place on the podium with a superbly-executed second, cutting in from the left and drilling a low shot just inside the left-hand post with just three minutes remaining .