AIK entered the competition in the previous round and made light work of Estonian side Paide Linnameeskond, winning the second leg 6-0 to complete an 8-0 aggregate victory.
The Solna side looked to be in for a similar night after the first quarter of their meeting with Gyor - they took the lead with less than seven minutes on the clock, as Erik Flataker set up Dino Besirovic.
With 21 minutes gone, Bersant Celina went on a wonderful run to evade the Gyor defence, cutting in from the left side of the penalty area before unleashing a right-footed stike to score a fine individual goal and put AIK 2-0 to the good.
Flataker and Besirovic were among the home players peppering the Gyor goal in search of a third, but thoughts of another home UECL thrashing were soon put to bed, as the Hungarian side gained a foothold in the game, carving out chances before the break through Nadir Benbouali and Mark Csinger.
The two sides continued to show plenty of endeavour after the break, but neither were able to create any real opportunities until 12 minutes from time when Gyor got themselves back in the match.
A corner delivered by Paul Anton was headed to the edge of the box, where Milan Vitalis had time to take it down and arrow a strike through the crowd and into the bottom corner of the net.
The home crowd encouraged their team to dig deep, not content with a one-goal lead to take to the second leg. They thought they had been rewarded in added time when Johan Hove met a flick-on at the back post and guided it home, only for VAR to rule he was a fraction offside.
2-1 to AIK was how it finished, with the tie to be finalised next week in Hungary.