Dzsenifer Marozsan's sweet strike and Lisa Sembrant's comical own goal put Germany 2-0 up early in the second-half before Stina Blackstenius gave Sweden a lifeline.
Sweden, who scored just three goals in their five games before the final, started more positively than their previous form suggested, but Germany started to impose themselves as time went on and the best chance of the half fell to Anja Mittag after 25 minutes.
Leonie Maier's curling shot was only parried by the Swedish keeper and the ball fell to Mittag just yards from goal but she blasted the ball high and wide.
The sides were evenly match but things changed in the second half and it was the Germans who deservedly took the lead three minutes into the second period.
When they did it was a goal worthy of a cup final. Dzsenifer Maroszan gathered a cross ball on the edge of the box and had time to steady herself before curling a perfect strike into the top right hand corner of the net.
They extended their lead 14 minutes later thanks to an unfortunate own goal. A Sara Daebritz free kick from 20 yards smacked the post and Linda Sembrandt tried to clear but instead kneed the ball into her own goal from just a few yards out.
Sweden reacted almost immediately and just five minutes later Stina Blackstenius pulled them back into the game. Olivia Schough hit a beautiful low cross into the box from the right and Blackstenius slid in between two defenders and poked the ball home to cut the deficit.
Schough had a great chance to level the scores three minutes from time to take the final into extra-time but her shot was blocked just yards from goal.