Only a minor miracle would prevent the Svenska Cupen winners from reaching the League Phase after their rampant 7-2 win at home in the first leg a week ago.
Though Etrit Berisha was called upon to make a save from the hosts' Lindon Emerllahu in the opening seconds, it was clear the crowd in Cluj-Napoca was not going to be treated to a similar goal-fest.
Silas Andersen had Hacken's only attempt on goal of the first half after 15 minutes, before a late rally from Cluj saw Lorenzo Biliboc strike the woodwork before Aly Abeid forced Berisha into action again.
Early in the second half, the home fans had something to cheer when Emerllahu's attempted pass to the right took a huge deflection and fell kindly for Adrian Paun in the centre, who took full advantage and slotted the ball into the bottom corner.
With six shots on target in the second half alone compared to one for their opponents, Cluj created enough chances to stage the most unlikely of comebacks, but following the goal, they found Berisha impossible to beat, as he denied substitute Louis Munteanu alone three times.
The 1-0 loss may not have been a vintage performance in Romania for Hacken, but they had already done more than enough to reach the League Phase with a 7-3 aggregate victory.
It marks the first time in two years that Hacken have reached a European competition proper, and will be hoping to do better than the six defeats from six they registered in the UEFA Europa League group stage in 2023/24. The draw for the UECL League Phase will be made tomorrow in Monaco.