The goal came in the 35th minute, when Danish Kasper Dolberg could finish on the edge of Häcken's penalty area.
The Hisingen team had opportunities to equalize, not least with 20 minutes left to play when Mikkel Rygaard came to a finish that was covered. But there was no Häcken goal and the loss was a fact.
Anderlecht's Swedish national team player Ludwig Augustinsson got no playing time in the match.
In a week, Häcken will have the opportunity to turn the double meeting around when they host Anderlecht at home.
In the first qualifying round, Häcken won against Spartak Trnava with 3–2 overall.
