Substitute Ezequiel Ponce struck the winner on the counter attack six minutes from the end of normal time as Roberto De Zerbi’s side failed to heed the signs after falling behind twice previously in the first half.
Joao Pedro equalised from the penalty spot in the first period then again in the second, both times after VAR had intervened in Brighton’s favour.
The hosts had the better of the play but they lacked the clinical edge of AEK, who scored with two excellent finishes from set-pieces. The first goal was a superb header from Djibril Sidibe, followed by a sliding finish from Mijat Gacinovic as Brighton were undone by nerves and their own naivety.
The opening goal came after 11 minutes and was against the early run of the play.
AEK’s first attack saw them win a corner on the left after a low cross was turned behind. As the ball was whipped in, no one had picked up the lurking Sidibe who with a late dash into the box caught Brighton out with a superb 15-yard diving header that whistled past Jason Steele.
De Zerbi’s side had been badly caught out, and seconds later it could have been two. Levi Garcia, who would torment Brighton in the first period with pace and clever movement, raced beyond the defence and went through on goal, but Garcia’s tame finish was too close to Steele.
Garcia wasted another glorious chance to double the lead from an almost identical position, this time slipping his effort just beyond the far post.
Pedro nodded wide from a free header inside the six-yard box as Brighton finally put together an attack to concern the AEK defence, but within a minute he had made amends for his profligacy.
When defender Ehsan Hajsafi dangled a leg as Pedro looked to cut inside to shoot the referee initially booked the striker for diving. But after a pitchside VAR review the booking was rescinded, Pedro stepped up and coolly rolled his penalty beyond Cican Stankovic to score Brighton’s first European goal.
At that stage it appeared that they had had their reprieve for the way they had left themselves vulnerable to AEK’s threat, but five minutes before the break there was another fine delivery from a set-piece and another critical lapse in concentration.
Brighton held a high line on the edge of their own box as a free-kick was whipped in from 40 yards out, but as blue shirts charged back towards their own goal none could prevent Gacinovic from sliding to get a foot on the ball to turn it beyond Steele.
There was still time for Jan-Paul Van Hecke to deny Orbelin Pineda what would have been a deserved third for AEK on the stroke of half-time.
There was relief then around the Amex when the referee was directed pitch-side for another VAR review after Pedro’s tumble inside the box under Damian Szymanski’s challenge had at first been waved on.
As in the first half, the decision was overturned, and Pedro got to his feet to replicate his earlier composed finish to draw Brighton level again.
De Zerbi was booked for remonstrating too forcefully on the touchline, before Pedro was handed the chance to seal his hat-trick and an opening night win when he spring the offside trap and went one-on-one with Stankovic. This time the goalkeeper got the better of their duel.
Then came AEK’s final sting. A raking ball from the back was nodded out wide by Ponce to Niclas Eliasson, who returned the ball to his fellow substitute. Although Steele blocked Ponce’s shot, the rebound ricocheted off the Argentinian and into the net for the winner.
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