The last matchday had seen Olympiacos grind out a 1-0 win over Kairat Almaty, and thus end a 10-game winless streak in the UCL.
With a pair of 1-0 wins following their last such run, they gave themselves the ideal chance of repeating history with a second-minute strike from Costinha, who headed in his first goal for two years at the end of a vicious outswinging corner from Rodinei.
As expected, though, Leverkusen rallied and nearly scored indirectly from a corner, with the ball fortuitously falling to Loïc Badé, only for his shot to be too weak to beat an unsighted Konstantinos Tzolakis.
Lucas Vazquez was then denied at Tzolakis’ near post, and the Greek stopper also pulled off an incredible save down low to his right closer to half-time, when Alejandro Grimaldo fired in a daisycutter after receiving a lay-off from Bade inside the box.
He blocked Christian Kofane at point-blank range almost on the stroke of the interval, too, and when Panagiotis Retsos cleared the ball, Rodinei received it. He burst downfield and found Mehdi Taremi on the charge, and the Iranian international delivered a powerful finish past Janis Blaswich.
That strike put Olympiacos on the verge of a first win in 14 clashes against Bundesliga opposition - a record that also contained 12 defeats.
For that reason, amongst others, a rally from Leverkusen felt inevitable, but Olympiacos’ work rate prevented Die Werkself from getting the momentum necessary to mount a fightback.
Indeed, Chiquinho wasn’t far from making it 3-0 via a direct free-kick attempt just before the hour mark, but there was a more attritional feel overall.
Retsos, in particular, was an assertive figure, with a well-timed and vital tackle against Grimaldo amongst his finer moments.
Aiming to succeed where Grimaldo couldn’t, Patrik Schick came painfully close to halving the deficit with 10 minutes to play, but again Tzolakis was alert in blocking him one-on-one when played through by fellow substitute Arthur.
Providing fresh legs from the other dugout, Giulian Biancone also had a moment to savour when taking the sting out of Malik Tillman’s low shot on 84’.
In the end, there was just no way through for the German giants, and like Olympiacos, they are vulnerable to elimination in next week’s league phase finale, when only a win will get them to the 11-point mark widely seen as a watershed to a top-24 finish.
The Greek heroes of Piraeus may yet fall short, but with them now sitting 22nd - and only being a point behind Leverkusen - simply avoiding defeat at Ajax might be just enough for them.
Flashscore Man of the Match: Konstantinos Tzolakis (Olympiacos)