Alexandre Lacazette's 81st minute goal proved the difference as Arsenal secured a vital away win over Olympiacos on Thursday.
The game was heading from a dour draw when the Frenchman popped up to score his second consecutive goal.
Bukayo Saka once again grabbed an assist when his cross found Lacazette in the box.
The result means Arsenal have kept three clean sheets in a row.
The return leg will be played at the Emirates on February 27.
Speaking after the game, Gunners keeper Bernd Leno said: "It's my job to make saves.
"At the end when you have a clean sheet, I'm happy. We won this game and we have the away goal so we're happy."