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.
Giorgos Masouras then headed over from close range – though he looked to be offside – before we finally began to come into the game.
Pierre-Emerick Aubameyang sent in a dangerous low cross which was just out of Alexandre Lacazette's reach, before the Frenchman shot wide after great build-up play involving Joe Willock and Gabriel Martinelli.
Overall though it was a cagey first-half, and it continued in that vein after the break, with neither side able to create too many chances.
Leno made a couple of smart stops, but when the home defence began to tire, we sprung into gear to break the deadlock in the final 15 minutes.
Goalscorer Lacazette could have doubled the advantage shortly afterwards, when a rapid counter-attack ended with our number 9 seeing his shot saved.
Sokratis thumped a late header against the bar but Mikel Arteta will be more than happy to take a one-goal advantage back to London.
HOW IT HAPPENED
WHAT IT MEANS
We take a narrow lead – and an away goal - into the second leg at Emirates Stadium next Thursday, as we look to qualify for the last 16 of the Europa League for the third consecutive season.
The second leg of this tie is next Thursday at Emirates Stadium, but before then we face Everton at home on Sunday, kick-off at 4.30pm (UK time).
This game kicked off at 10pm local time, so the team are spending an extra night in Greece before travelling back to London, as Arteta explained: "I believe that the first window - the first hour to hour and a half - is really important for the players to eat with the quality of nutrients that we need. I think it's better to do it in a hotel. It's better to rest in a bed, rather than stay in a flight when you are travelling and the next day, everybody does some recovery together and we fly back in the afternoon."
THREE THINGS WE NOTICED
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