Germany goalkeeper Nadine Angerer saved two penalties to help her side clinch the European Championship for the sixth successive time.
The captain denied Norway's Trine Ronning and Solveig Gulbrandsen in each half in the Stockholm final.
German substitute Anja Mittag scored the only goal of the game, finishing off a fine passing move.
Silvia Neid's Germany had to defend stoutly in the second period but have now won every tournament since 1993.
With a host of players absent through injury, Germany, with just six goals in six games in the tournament, have been far from dominant in Sweden.
But their youthfulness suggests they have a sound basis for yet another defence in four years.
Norway goalkeeper Ingrid Hjelmseth pushed on to the bar from a Nadine Kessler header inside the first minute and Germany striker Celia da Mbabi glanced wide from a Dzsenifer Marozsan corner.
Winners against Germany in the group phase, Norway were handed a fine chance to take the lead just before the half hour when Cathrine Dekkerhus went down in the area under minimal contact from Da Mbabi in the area, earning a penalty.
But Ronning tried to thump the spot-kick down the middle and Angerer saved with her legs.
Shortly after the interval, a sweeping move down the left saw Da Mbabi clip the ball across for Mittag, who had only been on the pitch for three minutes, to put the Germans in front.
Norway were given a second opportunity from the spot when Caroline Hansen was tripped by Jennifer Cramer but Angerer, who saved a penalty in German's World Cup final win over Brazil in 2007, got a hand to Gulbrandsen's effort to preserve her team's lead.
As Norway pressed, Ada Hegerberg had a strike correctly ruled out for offside before Kessler hit the post for the Germans in the closing stages.