In the first half, Häcken held the defensive together impressively.
They tried to take advantage of counterattacks and set pieces, but at the break it was goalless.
In the first quarter of the second half, however, they could not resist any longer.
First it was the star Lieke Martens who was in the right place when the Häcken players misjudged a cross and then the in-form Kadidiatou Diani scored 2-0.
Diani has now scored in five straight games.
After that, Häcken had to bet forward, which gave spaces for the visiting French sisters.
The 5118 people in the crowd continued to cheer for their team, but there were no more goals in the match.
With Rosengård making it to the Champions League group stage, Sweden will be represented this autumn by a team there.
Last season, Häcken was the only blue-yellow team in the tournament.