Elfsborg had a 1-0 lead against Sheriff Tiraspol after the match in Transnistria.
When the return match kicked off at Borås Arena, the home team needed less than a minute to take the lead.
Jalal Abdullai was able to exploit a defensive mistake by Sheriff and roll the ball into the opponents' net.
In the 73rd minute, Michael Baidoo scored the final result to 2-0, which means 3-0 Elfsborg overall and advancement in the Europa League qualifiers for the Borås club.
In parallel, Djurgården played in the Conference League qualifiers.
Progrès Niederkorn, from Luxembourg, scored a goal after three minutes and Jacob Une Larsson was sent off in the 36th minute.
But Djurgården, who had a 3-0 lead from the home match, was able to hold on despite the tough start. The match ended 1-0.
In the next qualifying round, the Stockholm team will face Finnish Ilves Tammerfors, who knocked out Austria Wien in the second qualifying round.
