Arsenal takes a two-goal lead and three away goals into the second leg at home.
The Gunners did their best to fire on and they have one foot placed firmly in the Europa League quarter-finals.
It looked like being the same old story for Mikel Arteta’s side when a calamitous error by Dani Ceballos allowed Olympiacos striker Youssef El-Arabi to cancel out Martin Odegaard’s thunderous first-half opener.
Gabriel nodding in from a corner and Elneny blasting in a third from a distance to give the scoreline a comfortable feel.
“We are happy with the result, with the goals and the way we played in big seconds of the game,” the Arsenal boss said after Thursday night’s win.
“But as well, we have to be very clear and honest with ourselves. We gave three goals to the opponent, they took one and at this level, they are going to punish you.
“If we want to go to the next level we have to stop doing that and be more ruthless. When you are that dominant and playing that well, just kill the game.”
Especially what happened against Burnley at the weekend when Granit Xhaka gifted an equaliser to Chris Wood, you would have thought the Gunners would have learned their lesson when it comes to taking risks while playing out from the back.
But in this case of deja vu Ceballos was the culprit this time around.
There had already been alerting signs in the first half, with David Luiz almost handing the hosts an equaliser after Odegaard had opened his Arsenal account with a powerful drive from a distance which flashed past Jose Sa.
The visitors played their way into trouble again 13 minutes into the second half and this time they weren’t so lucky.
Arteta will certainly have been delighted with the way his team responded to Ceballos’ mistake.
With memories of last season’s painful exit to the same opponents still fresh, taking only a 1-1 drawback to the Emirates Stadium would have set alarm bells ringing.
But two precious goals in the closing 11 minutes now mean Arsenal head home with some much-needed breathing space.
Gabriel got the second of the night with a fabulous header from Willian’s deep cross and then Elnney – who had just replaced Willian – crashed home a superb strike from 25 yards which fizzed in off the post.
Arsenal knows they now have a great opportunity to book a spot in the quarter-finals.
Olympiacos face Larissa in their last league game of the season next, while Arsenal host Tottenham in the north London derby as they return to Premier League action.