Following their 6-0 win in Enschede, FC Twente started the match in Slovakia with an altered XI, giving the likes of young Lucas Vennegoor of Hesselink and winger Younes Taha a start.
It took the dominant Dutchmen just seven minutes to score in Slovakia as well, with Max Bruns nodding in a corner from Daouda Weidmann to open the scoring. Twente continued controlling the game, but could not get a second before the break.
Marko Pjaca eventually doubled the lead after nearly an hour, burying the ball in the far corner of Filipe's goal.
Dunajska Streda weren't done fighting in front of their home crowd and scored their first goal of the tie five minutes after Pjaca's 2-0 - Abdoulaye Gueye tapped in after poor defending from Ruud Nijstad. Klemen Nemanic levelled ten minutes later, heading in from a corner to keep the second leg mildly exciting.
The hosts completed an unlikely comeback when substitute Prince Owusu got Dunajska Streda in front in the 87th minute - the Ghanaian forward received a sublime pass from Giorgi Gagua, outplayed goalkeeper Joel Drommel and put the ball in an empty net.
The home crowd were ready to celebrate a meaningless win when Marko Pjaca struck a second time, this time seconds before the full-time whistle as the Croatian profited of a costly mistake from Filipe.
A weak FC Twente failed to further help the Dutch coefficient, only managing a 3-3 draw away at Dunajska Streda. In the UEFA Conference League play-offs, FC Twente will face Azerbajani giants Qarabag on August 20th and 27th.