Any hopes Hearts had of salvaging the tie were effectively over after 29 minutes when midfield player Julian Brellier picked up two bookings in the space of five minutes - his first for coming onto the field without permission after treatment.
He received his marching orders after challenging for the ball with his arm raised and it left the visitors short handed.
Hearts were reduced to nine men after 63 minutes when Neil McCann has shown a straight red card for a two-footed challenge on Vladimir Ivic.
Valdas Ivanauskas sprang a surprise before kick-off when he started with teenage striker Jamie Mole, who is yet to start an SPL match.
Paul Hartley also started his first game of the season, while AEK brought in goalkeeper Dionisios Chiotis for Stefano Sorrentino, hurt in a car accident at the weekend.
AEK started strongly and Liberopoulos was only a yard too high with a shot before Pantelis Kapetanos missed the target with a free header from six yards.
Hearts hit back and Mole slipped the ball past Chiotis, but Nikos Georgeas was on hand to boot it to safety.
Hartley then missed the easiest of opportunities when he headed straight at Chiotis after a great flick from McCann.
AEK also had their chances and Panagiotis Lagos shot straight at Craig Gordon when he was clean through and Liberopoulos somehow sent a header wide from just three yards.
It was backs-to-the-wall stuff in the second half for Hearts but, for all their possession, AEK did not show too much adventure in front of goal.
Four minutes after McCann was sent off Liberopoulos had another shooting chance, but it was a comfortable save for Gordon.
The breakthrough eventually came when Deividas Cesnauskis fouled Vasilis Lakis in the penalty box in the 79th minute and Julio Cesar fired the spot-kick high into the net.
Liberopoulos then made it 2-0 with a head-flick from ten yards, before Julio Cesar took advantage of slack play from Edgaras Jankauskas to lash home the third from 16 yards.