The Dons moved into the third qualifying round of the Europa Conference League despite a 2-0 defeat by 10-man BK Hacken.
Aberdeen progressed to a clash against Breidablik thanks to a 5-3 aggregate win, after the Icelandic side shocked Austria Vienna with a 3-2 victory over two legs.
Second-half goals from Martin Olsson and Leo Bengtsson gave the Swedish side hope but a red card for Patrik Walemark undermined the hosts' comeback.
Aberdeen beat Real Madrid in the European Cup Winners' Cup final on a similarly wet evening in Gothenburg 38 years ago and a first-leg display that rekindled memories of their 1980s heyday set up the chance to enjoy a happy return.
They had plenty of chances to secure a better result but it was job done in the end.
Stephen Glass' side survived some early pressure before beginning to dominate.
Christian Ramirez had several chances, producing a fresh-air swipe from the first, being denied by the goalkeeper after a clever Jay Emmanuel-Thomas through ball and then having a curling effort held.
Emmanuel-Thomas came closer after good skill in the box and a shot that drew a smart stop from the goalkeeper.
Lewis Ferguson had an excellent header pushed away from the corner as the Dons ended the half on top. But they suffered an early blow after the break when Emmanuel-Thomas went off with a clash of heads. Brighton loan player Teddy Jenks came on.
Hacken took the lead in the 51st minute when Olsson played a slick one-two and finished well after sloppy possession play from the visitors.
Funso Ojo soon missed a glorious chance to level on the counter-attack when he completely missed his kick under no pressure from eight yards following a square ball by Ramirez.
Joe Lewis soon made a brilliant one-handed stop but the Swedes moved two ahead midway through the half after catching Aberdeen out with a ball through the middle of the Dons centre-backs with Andy Considine appealing in vain for offside.
Lewis tripped Bengtsson and the midfielder sent the goalkeeper the wrong way from the spot.
Walemark soon had a minute of madness though, getting booked twice in quick succession, the latter time for catching substitute Jack MacKenzie in the face with an elbow.
There was a string of yellow cards for both sides including one for Glass and another for Declan Gallagher - before the defender came on for his Aberdeen debut - with seven players booked in addition to Walemark.
The pressure was off Aberdeen now and they came close to scoring on several occasions.
Ferguson saw a free-kick pushed wide, Considine could not turn home a driven ball from Ramirez, and substitute Jack Gurr had an effort saved.