Having won this fixture 2-0 in the league phase, the hosts started on the front foot, with Mehdi Taremi slamming an early chance wide after bringing down a long ball.
At the other end, Schick was denied at close range and Ernest Poku drilled across goal and wide of the far post, before the Greek side landed their first shot on target through Gelson Martins, only for his fizzing strike to be expertly tipped around the post.
Konstantinos Tzolakis then pulled off an even better save for Jose Luis Mendilibar’s men, as he somehow diverted Ibrahim Maza’s volley onto the bar from point-blank range.
Poku then poorly dragged off target after being set through one-on-one, before the visitors received a huge let off on the stroke of half-time as Ayoub El Kaabi’s deft finish was ruled out for offside following VAR intervention.
Olympiacos, who last reached the Round of 16 of this competition in 2013/14, came out of the blocks quickly after the break, with Martins firing narrowly over the bar from 25 yards and Giulian Biancone also ballooning a header off target.
They could have been punished for those misses by Alejandro Grimaldo, though his tame strike was straight at Tzolakis, but Die Werkself did not have to wait too much longer to break the deadlock, as Schick ran onto Poku’s beautifully threaded pass and kept his composure to bend past the goalkeeper.
Within three minutes, the striker doubled his tally for the night, as he was criminally left unmarked from a corner and flicked a header home for his fourth goal in as many matches, although Tzolakis will have felt he could have done more to save.
Apart from substitute Lorenzo Scipioni curling over, that killed off the game, with the sting well and truly taken out of the Red and Whites’ performance as they extended a poor run of form to one win in five.
Leverkusen, on the other hand, saw Schick miss a further chance, but have now won six times in seven outings since losing to Olympiacos in January, with this latest success ending a run of four trips to Greece without a win.
Flashscore Man of the Match: Patrik Schick (Bayer Leverkusen)