Brighton began the game in control, but the focus shifted to AEK as the half ticked on and the hosts almost took the lead inside the first 20 minutes when Mijat Gacinovic got the better of Lewis Dunk but fired his shot into the side netting.
AEK carved out the next couple of chances in quick succession after an initial attempt was blocked, Orbelin Pineda took a shot from the edge of the area, which Bart Verbruggen spilled but pounced on before any of the opposing strikers were able to make him pay.
The hosts bossed the second half of the first period and carved out their best chance of the game five minutes before the interval when Steven Zuber beat Joel Veltman and saw his shot deflected onto the upright off a sliding Dunk before Gacinovic put the rebound wide.
Brighton headed down the tunnel lucky to be level and many would likely agree that it was one of the worst halves of football we had seen from the Seagulls in a long while.
Matias Almeyda's side started the second half on top as well and got the first big chance of the half as Gacinovic fired a first-time shot from a cutback, which Verbruggen palmed over the crossbar.
Ten minutes after the restart and completely against the run of play, Pedro burst into the opposing box and went down, but the referee waved play on.
However, after a fairly quick review, VAR invited Sandro Scharer to take a look at the replay, and the match official reversed his decision, awarding the Seagulls a penalty.
Pedro picked himself off the turf and stuck the spot-kick away to become the third player to successfully convert four penalties in a single European season for an English club, sharing the record with John Wark, who achieved the feat for Ipswich Town in 1980-81, and Bruno Fernandes in 2020-21.
It was also his fifth goal in Europe, giving him the lead in the top goal scorer standings in this competition.
With that goal, Brighton have now found the net in 31 of their last 32 matches in all competitions, failing only to score against Chelsea back in September.
Matters got worse for the hosts after that as Gacinovic, who was arguably one of their best players in the first half, was shown a second yellow of the evening after catching Veltman with a needless tackle in the 65th minute.
Brighton looked a lot more comfortable with a goal and man advantage, and it began to feel like it was their match to lose.
Evan Ferguson almost put the match to bed 15 minutes from time as he tried to round the keeper but Cican Stankovic made himself big and did very well to deny the Brighton striker.
It was all Brighton in the closing stages of the match and while they are assured of a spot in the knockout round, they will still need to beat Marseille in their final group-stage match to avoid a knockout playoff.
Roberto De Zerbi's side will return to Premier League action on Sunday with a trip to Stamford Bridge, while AEK will be back at this venue to take on Aris.