Celia Okoyino da Mbabi raced down the left wing and passed to substitute Anja Mittag, who scored in the 49th minute at Friends Arena in Solna, located just north of Stockholm.
Norway failed to score with two penalties. Germany goalkeeper Nadine Angerer saved Trine Ronning’s spot kick in the 29th and denied Solveig Gulbrandsen in the 61st.
In the 64th minute, Norway’s Ada Hegeberg scored a goal that was disallowed for offside.
Angerer played down her own role after the match, saying Germany’s success was the result of teamwork.
“Penalties are all about luck,” she said, adding they are “easier for a goalkeeper” than the player shooting.
“We have a good team spirit, I don’t think we have space for individualistic flair. That’s why we are getting better and better.”
Germany has won the past six European tournaments. In the semifinals, the Germans defeated Sweden 1-0 and Norway beat Denmark 4-2 in a penalty shootout after it was 1-1 following extra time.