The only time that AEK have overturned a 3-0 first leg deficit in a European tie was against a Queen's Park Rangers side featuring the likes of Gerry Francis and Stan Bowles, but a raucous home crowd were soon dreaming of 1977 once again after an extraordinary first half.
However, it could have been very different had Rayo’s Andrei Ratiu taken his chance in the fifth minute, but the Romanian somehow poked his effort wide from six yards with the goal at his mercy.
More than just a stay of execution, Rațiu’s miss was the catalyst for a remarkable fightback.
In the 11th minute, Zini hammered home the opening goal of the match from eight yards out, as the Angolan easily overpowered Rayo midfielder Pathe Ciss to latch onto a long throw into the box.
Just over 20 minutes later, Ratiu continued his calamitous night, this time bringing down Aboubakary Koita in the penalty area after a mazy run from the Mauritanian.
AEK captain Razvan Marin stroked home the penalty to reduce the deficit to one, and the Romanian almost completed the comeback on the stroke of half-time, but his rasping long-range drive was tipped over by Rayo goalkeeper Augusto Batalla.
The break offered no respite for the beleaguered and shell-shocked Spanish side, as six minutes after the restart Zini rose to meet a Dereck Kutesa delivery, and the Angolan’s glancing header looped beyond Batalla into the far corner.
Having offered little going forward, few could have seen a Rayo goal coming, but less than 10 minutes after surrendering the lead of the tie, they were back in front on aggregate.
Isi Palazon found a pocket of space from which to drive into the AEK box, and his exquisite finish put the Spaniards back in charge of the tie.
On a night of endless drama, the closest the home side came to once again getting themselves level was on 66 minutes.
Pacha Espino inexplicably dallied on the ball in his own box, allowing Lazaros Rota to steal the ball and drill a low cross into the six-yard box, where Zini failed to rearrange his feet and apply the finishing touch from just two yards out.
It would prove to be the last moment of hope for the Greek side, on a night where their remarkable comeback fell just short, leaving Rayo to progress to a first-ever European semi-final.