Despite dominating, the reigning Swedish champions' away match against Gibraltar's Lincoln ended 0-0 on Tuesday night.
But after Mjällby won the first leg of the two-legged tie 3-0, the team advanced to the next qualifying round.
It is now clear that the club will be allowed to play in a European league phase, but it remains to be seen whether it will be in the Champions League, Europa League or Conference League.
In the third qualifying round, they will face the winner of the match between reigning Georgian champions Iberia Tbilisi and reigning Slovak champions Slovan Bratislava. That match will be decided on Wednesday at 20:15. Slovan Bratislava leads 2-0 after the first leg.
