The Reds fielded a strong lineup that saw the return of England quartet Raheen Sterling, Daniel Sturridge, Steven Gerrard and Glen Johnson as well as a debut for new signing Lazar Markovic against an Olympiakos side who were laying their second group game after an opening 3-0 win against AC Milan.
Boosted by the return of most of their World Cup representatives. Liverpool came close to a superb start as Gerrard swept in a dangerous free-kick in the fourth minute only to see it blocked by the defence. The Liverpool captain's effort served as a warning of things to come soon after, Sturridge aimed for goal but his shot found the oncoming Sterling who slotted past Megyeri to open the scoring.
Gerrard came close to adding a second for Liverpool in the 22nd minute when he sent a thundering effort towards the goal but saw the end product go wide of the target but Liverpool continued to pressure and a well-worked combination between new signings Markovic and Can saw the former sweep a curling shot at goal that came achingly close to dipping under the bar.
Olympiakos had a good chance of their own just two minutes later as Saviola looked to test Jones in the Liverpool goal but saw his shot blocked by Enrique who put the ball behind for a corner and from the resulting set-piece, Diamantakos had a chance but saw his effort drift wide of the target.
An array of changes for both sides saw Robinson, Coutinho and Allen come on for Liverpool in place of Enrique, Can and Markovic but it was the Greek side that had the best start to the second half as Ghazaryan tested Jones with a poweful shot that beat the Australian but cannoned back off the crossbar.
Liverpool responded with a chance for Coutinho but his effort went over the crossbar and the Brazilian had another good chance with 13 minutes to go as he struck from long range with a powerful effort that narrowly went past the post.
Olympiakos should have been level in the 80th minute when a mazy run from Bouchalakis saw him scythe through the Liverpool defence and even swish past Jones but a stunning chase back from Coates prevented the Greeks from drawing level.
Liverpool held on for the win despite a late chance from Samaris that drew a fine save from Jones but the Reds could have ended the game with a two-goal victory as Ibe looked to pick out Lambert only for the England striker to his a shot just past the near post.