Ciani's goal proved enough to keep up Bordeaux's unbeaten run in Europe
French champions Bordeaux made it six Champions League victories in a row with a hard-fought triumph in Greece.
Centre-back Michael Ciani rose unchallenged to head home a Yoann Gourcuff free-kick and put the visitors ahead on the stroke of half-time.
The Greek champions nearly equalised in the closing stages when Lomana LuaLua's shot was tipped around the post.
And moments later, Enzo Maresca's header was ruled out for a foul on the goalkeeper by Matt Derbyshire.
With former France captain Laurent Blanc at the helm, Bordeaux are taking the Champions League by storm this season.
They dropped just two points in a group which included Bayern Munich and Juventus, beating the German giants home and away.
Victory in Athens only adds to their growing reputation. The Greek champions had won their last five European home games - including a 1-0 victory over Arsenal - and had conceded just one goal in their previous six outings.
The home side made the brighter start in the first ever meeting between these teams.
Former Aston Villa defender Olof Mellberg rose to meet Jesus Datolo's free-kick but planted his header wide of the post.
Olympiakos goalkeeper Antonis Nikopolidis, making his 100th European appearance, was rarely troubled in the first half as the French side, missing injured skipper Alou Diarra, struggled to gain a foothold in the game.
But all that changed when English referee Howard Webb awarded a controversial free-kick two minutes into stoppage-time.
Webb blew his whistle even though former Newcastle striker LuaLua appeared to take the ball cleanly from Benoit Tremoulinas.
Gourcuff's delivery was inch perfect for Ciani to nod home from six yards.
Bordeaux remained on the front foot after the break and almost went 2-0 up when an unmarked Ciani headed a corner over the bar.
Derbyshire's introduction sparked a late flurry from Olympiakos
Bozidar Bantovic, Olympiakos's third manager this season, handed ex-Blackburn forward Derbyshire his Champions League debut in a bid to salvage something from the first leg.
And the Englishman made an instant impact, neatly laying the ball off for LuaLua, whose low shot was tipped around the post by Cedric Carrasso.
In a frantic finale, Fernando hacked Ieroklis Stoltidis's effort off the line before Maresca jumped to head home after a sliced clearance by Ciani, but Webb disallowed the goal because Derbyshire had impeded Carrasso.
The decision ensured Bordeaux hold the advantage going into the second leg in France on 17 March.
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