AIK were cruising to victory in the first leg, before Gyor grabbed themselves a lifeline to take just a 2-1 deficit into the return meeting in Hungary.
If the Swedish side needed reminding that the tie was still very much alive, they got one in the opening minutes when Claudiu Bumba powered a half-volley towards goal, which goalkeeper Kristoffer Nordfeldt managed to tip onto the crossbar.
With 34 minutes on the clock, Gyor took a deserved lead when a deep cross from Daniel Stefulj on the left was cushioned home on the volley by Zeljko Gavric to level the aggregate scores.
The home side's pressure didn't wane, and on the half-hour mark a corner was played to Stefulj at the edge of the area, and he proved his volleying technique was on point too, as his powerful effort had to be beaten away well by Nordfeldt.
Soon after, Gyor thought they had a penalty after a pullback by Dino Besirovic, only for VAR to deem that contact had been made outside the area and change the original decision.
AIK's luck with decisions, however, seemed to have run out in first-half stoppage time when Aron Csongvai's corner was headed in by Filip Benkovic, but the goal was disallowed for the centre-back climbing on his marker.
But luck was back with the Solna side in the opening minutes of the second half, as a foul by Mark Csinger inside the area gave AIK a penalty and the perfect opportunity to restore their aggregate advantage.
However, Anton Saletros stepped up and has his spot-kick saved by Samuel Petras.
On the hour mark, things went from bad to worse for the visitors when Paul Anton swung in a corner, which Csongvai diverted into his own net for 2-0 on the night, handing the lead in the tie to the Hungarian side.
With a quarter of the match to go, Anton's deliveries were still causing AIK problems, this time a free-kick from out wide was headed just over by Nadir Benbouali.
The second goal seemed to have knocked the stuffing out of AIK, who created little going forward until the final minute, when a ball was half-cleared to Eskil Edh on the edge of the area, and his thunderous strike cannoned off the underside of the bar and bounced out.
That very near miss meant it is Gyor who move on to the Playoff Round, while AIK's wait to reach a UEFA competition proper since 2012/13 goes on.