Liverpool had early chances from Anthony Le Tallec, who shot high and wide, and Vladimir Smicer who's shot was fired straight at the keeper.
Michael Owen did put the ball into the back of the net after a goalmouth scramble but it was disallowed for offside.
Harry Kewell has been booked for dissent after a foul on Rudonja.
Igor Biscan also had a chance from a corner, but the keeper got down well to save from his header.
Olimpija had a chance early in the second half but Dudek saved well.
Smicer had another shot on goal, but failed to beat the keeper.
Kewell then forced a great save from the keeper with e curling left-footed free kick to the far post.
An error from Steven Gerrard allowed Zlogar in to shoot beyond Dudek and put the home side ahead on 66 minutes.
Emile Heskey had a chance to equalise from a Gerrard free kick, but headed over the bar.
Kewell then came close but the keeper turned the ball around the post for a corner.
Owen finally got the equaliser and became Liverpool's highest ever scorer in European football when he headed Riise's cross into the back of the net on 77 minutes.
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Team: Dudek, Diao (Finnan 69), Hyypia, Biscan, Riise, Murphy (Gerrard 15), Smicer, Le Tallec (Welsh 87), Kewell, Owen, Heskey.
Subs: Luzi Bernardi, Henchoz, Traore, Sinama Pongolle.