Lea Schüller's first goal came already in the eighth minute when Jennifer Falk was responsible for a failed equipment.
Schüller pushed in the lead goal in front of the home crowd and the Häcken goalkeeper was cracked.
Just two minutes later, the same Schüller nodded in 2-0 and the uphill was solid for the Swedish champions.
Bayern, with national team players Sofia Jakobsson and Hanna Glas in the team, continued to dominate and with just under half an hour played, the post saved Häcken from falling behind by three.
With less than 20 minutes left to play, Linda Dallmann made it 3-0 when she shot the ball through a Häcken player.
It was not the end there either, but in extra time the Serbian Jovana Damnjanovic finished a post and fixed the result to 4-0.
Sofia Jakobsson was replaced after just under an hour and Glas was replaced with ten minutes left to play.
Häcken is last in the group with zero points and so far they have not managed to score.
The next match is away against Portuguese Benfica on November 10.