Progressing into the next round was a relatively straightforward task for Juan Ignacio Martinez's side after their comprehensive 3-0 win in Valencia in the first leg, and despite their opponents being roared on by 29,000 fans in the Georgios Karaiskakis Stadium, they started the brighter of the two sides.
Jose Barkero fired their first warning shot, striking the ball just over the bar from outside the area in the second minute.
Paulo Machado responded immediately for the hosts with a long-range effort that went wide of Keylor Navas' goal but the tie was all but killed off when Martins struck after nine minutes.
The Olympiacos defence naively left the Nigerian striker completely unmarked while facing a corner, allowing him to nod Barkero's cross into the back of the net from the middle of the six-yard box.
The goal meant the Greeks needed to score five times without reply if they were to progress, and although Spanish coach Michel's side did not give up trying to find the net at least once, their efforts were in vain.
The closest they came to a goal was from an injury-time header by centre-back Dimitrios Siovas that was destined for the bottom corner of the Levante goal, but Navas produced an outstanding diving save to keep the effort out and maintain a clean sheet on the night and over both legs.
Levante can now look forward to a last-16 tie with Russian side Rubin Kazan, who knocked out the holders Atletico Madrid.