Alexandre Lacazette scored a precious late winner as we edged a cagey first-leg encounter in Athens.
In a closely-fought affair, the Frenchman tucked home from close range after good work by first Pierre-Emerick Aubameyang, then Bukayo Saka inside the box, to silence the intimidating home crowd.
It was something of a smash and grab raid after we had absorbed pressure for much of the game.
In fact Olympiacos nearly opened the scoring inside just two minutes, but Bernd Leno was alert enough to turn Mathieu Valbunea's goal-bound volley away from danger.
The Greek fans hardly needed lifting, but their fast start only raised the volume levels further inside the sold-out Georgios Karaiskakis Stadium.