Ferencvaros came into this game knowing that a victory would secure their place in the round of 16 play-offs, and the Greens took no time in getting their noses in front, taking just nine minutes to score the opener.
Adama Traore delivered a phenomenal inswinging cross to Mohamed Ali Ben Romdhane at the back post, where the Tunisian forward lept above the defence to fire a bullet header into the top-left corner.
Traoré went from provider to goalscorer with 34 minutes on the clock too, with the Mali international playing a lovely one-two with Alex Tóth before firing a thunderous strike off the crossbar and into the net from outside the penalty area.
The Greens appeared to have wrapped up the victory before the break, adding a third goal with just added time remaining. Romdhane was the goalscorer yet again, this time heading into the bottom-left corner from a delightful floated cross from Mohammad Abu Fani.
The hosts seemed more than content to sit back and protect their three-goal advantage after the break, with the Hungarian champions having very little possession but limiting AZ to no shots in the opening 25 minutes of the half.
Maarten Martens side did manage to pull a goal back with 14 minutes remaining after Kees Smit played a stunning ball to Sven Mijnans who rifled a first-time effort into the top-left corner to give AZ a glimmer of hope.
That slight tinge of hope was snatched from their grasp just six minutes later, when the hosts were awarded a penalty after Seiya Maikuma handled the ball in the penalty area. Barnabas Varga was the man who stepped up to take the spot-kick, and the striker kept his cool to slot the penalty into the centre of the goal.
The visitors fired in a late consolation goal in the 90th minute through Troy Parrott, as the Irish forward bent a lovely right-footed finish inside the right post.
AZ then struck again in the 95th minute, through Mijnans again after the young midfielder fired home from the centre of the box into the bottom-right corner. However, Keane’s men saw the game out from there to book their place in the round of 16 play-offs.
AZ also advanced to the round of 16 play-offs despite their humbling defeat, having now failed to win any of their last three away games (D2, L1).
Flashscore Man of the Match: Mohamed Ali Ben Romdhane (Ferencvaros)