The Welsh club had held a 5-1 lead after their handsome win in the first leg of this play-off tie last week.
The hosts never looked capable of turning the contest on its head but they did take the lead on the night through Njongo Priso's 73rd minute strike.
Substitute Roland Lamah responded instantly, but Hamza Younes headed home the winner for the hosts before Swansea captain Leon Britton was sent off late on.
Michael Laudrup's side can at least look forward to at least another six games in their European adventure, and they will find out their opponents when the group stage draw is made on Friday.
But the Dane will have been concerned with several aspects of this sluggish performance.
As with the previous round against Malmo, Swansea were nowhere near as effective as they had been on home soil, and it is an issue that will need to be rectified if they are to advance beyond the group stage.
After labouring for much of the game, Swansea fell behind on the night with 17 minutes to play.
The Swans' back four attempted to play Priso offside, but Angel Rangel kept the Cameroonian onside and he easily beat Gerhard Tremmel.
Swansea hit back just a minute later. Alejandro Pozuelo found Lamah unmarked and in acres of space, and the winger finished superbly to claim his first goal for the club.
Source: PA
Source: PA