Anja Mittag got the goal for Germany when she capped a fine passing move in the 49th minute - the game's one true moment of magic ultimately deciding it - but goalkeeper and captain Nadine Angerer was the hero as she saved a penalty in either half.
Norway knew it was not to be their day when they then saw Ada Hegerberg's strike ruled offside midway through the second half
Germany had looked the most threatening side throughout, creating more and better opportunities in either half.
Celia Okoyino da Mbabi had two great openings within the space of two minutes, first scuffing a shot when it was laid on a plate by Nadine Kessler and then heading wide when she met Simone Laudehr's corner at the near post.
Da Mdabi then made an impact at the other end when she brought down Cathrine Dekkerhus in the area.
However, she was bailed out by Angerer, who adjusted mid-flight to get a knee to Trine Ronning's spot-kick and turn it away.
Germany's goal arrived early in the second half and when it did it lit up the stadium, with a series of first-time passes allowing Laudehr to release Da Mdabi down the left wing.
She pulled the ball back and Mittag, left all alone by a Norwegian defence pulled this way and that, finding time and space to fire first-time inside the right-hand post.
Norway soon had another chance from the penalty spot when Caroline Hansen went to force her way between Jennifer Cramer and Dzsenifer Marozsan and was sent sprawling in the process.
Solveig Gulbrandsen took responsibility this time but the result was the same as Angerer punched it firmly clear.
Norway thought they had an equaliser in the 65th minute when they broke down the left and Hansen crossed for Hegerberg to turn it in, but assistant Sian Massey waved for offside and Norway's frustration grew.
They went close again moments later when Elise Thorsnes beat Angerer to get on the end of a long ball and try to poke it home, but the ball bounced agonisingly wide before Angerer received treatment following the collision.
Kessler might have capped it eight minutes from time when Toril Akerhaugen got her positioning all wrong and allowed Leonie Maier's tame cross to roll towards the penalty spot, but although Kessler's scuffed shot eluded the outstretched limbs of some desperate defenders, it rolled on to the post and away.
It proved no matter as Germany hung on to continue their remarkable run of dominance in this competition.