FC Twente aimed to return to the UEFA Europa League for the second time in 13 years with Wout Weghorst as their starting striker - the Netherlands international joined the team on a free transfer after his Ajax contract expired in June.
It were the hosts who nearly dealt the first blow through Weghorst, who failed to convert after Daan Rots found the striker in the box.
Ferencvaros took over from the tenth minute on, creating a handful of small chances before Twente captain Bart van Rooij misjudged a ball and let himself get surprised by Lenny Joseph, who creeped past the right-back and tapped the ball past Lars Unnerstall for the opener.
FC Twente took over again on possession, but failed to create many chances until Sondre Orjasaeter dribbled past his opponent and found newcomer Aske Adelgaard, who neatly slotted the ball in the far corner for the 38th-minute equaliser.
The Hungarian visitors opened the second half with a pocket of chances, but couldn't hang onto the ball much longer and relinquished control back to FC Twente, who tried their luck via Orjasaeter and Thomas van den Belt, but were rejected by Denes Dibusz.
After Kristian Hlynsson got close one more time for Twente, Ferencvaros swooped in like a seasoned European side and controlled the game in crunchtime. Lenny Joseph got close twice earlier and again in the 80th minute, when the Haitian forward was left alone by Twente defenders in the box and was free to prod in Callum O'Dowda's cross.
Twente tried, but failed to level the score before full-time and will have to make up a one-goal deficit in Budapest next week, when Ferencvaros host the Eredivisie side on Thursday, July 30th.