Four of the five goals came in the first half with Suarez and Milan Jovanovic putting Anderlecht 2-0 up before AEK pulled one back through Leonardo.
Suarez found the back of the net again just before the break to make it 3-1 and then, after AEK had lost Kostas Manolas to a red card with 12 minutes remaining, the Argentinian striker completed the scoring with his third goal late on.
Anderlecht, who won the 1983 UEFA Cup and also finished runners-up the following year, beat AEK 3-0 at the Constant Vanden Stock Stadium at the group stage of last season's competition and the Brussels-based club were on top from early on.
Suarez and Lucas Biglia both tried their luck before the former opened the scoring in the 16th minute with a low shot past AEK goalkeeper Dimitrios Konstantopoulos.
AEK tried to hit back and Leonardo brought a save out of Silvio Proto in the home goal with a drilled shot in the 24th minute.
The visitors found themselves 2-0 down in the 33rd minute though when Serbia international Jovanovic got on the end of Fernando Canesin's right-wing cross to plant a header past Konstantopoulos.
That gave Anderlecht some breathing space but that advantage lasted barely two minutes before AEK pulled a goal back with a superb strike from Leonardo.
Unfortunately for the Greek side, they too were hit by a quickfire response before they could build any momentum as Anderlecht restored their lead four minutes later with a fine goal of their own, Suarez.finding the top corner of the net from the edge of the box.
The second half saw Anderlecht pushing to extend their lead and Jose Carlos Fernandez and Jovanovic both had efforts before AEK were reduced to 10 men in the 78th minute when Manolas picked up his second yellow card of the half.
Anderlecht quickly made the most of their numerical advantage to net a fourth goal in the 84th minute, with Suarez completing his hat-trick with a close-range finish from Sacha Kljestan's pass.