Liverpool's belief that they are well-nigh unbeatable on home soil carried them through the wind and the rain here last night and into the last 16 of this season's UEFA Cup.

But, in a tournament now awash with Champions League drop-outs far greater, far more demanding, tasks do lie ahead for Britains sole survivors.

Gerard Houllier had been somewhat apprehensive in the days leading up to this game, an understandable reaction bearing in mind the squandered opportunities and criminal wastage of the tie's first leg in Athens a fortnight earlier.

On paper at least, a 2-2 draw against a group of players who have come to regard victories on home soil as the inevitable byproduct of pulling on their boots was highly commendable but Houllier made little or no attempt to conceal a sense of disappointment which, in truth, verged on outrage.

Liverpool's superiority in that first game was so pronounced, the class divide between the sides so glaringly apparent, that Olympiakos' knee-jerk response was to dispense with their coach Yiannis Matzoyrakis.

As Matzoyrakis had been at the helm for just seven months and had led his team to the Greek title last season, he had every reason to feel somewhat aggrieved.

Even so, Houllier did not feel inclined to gamble. Indeed, his team selection hinted - rather broadly - at over-caution for, with both Michael Owen and Robbie Fowler left on the substitute's bench, there was a palpable sense that the Merseysiders were quite prepared to hold what they had.

Not that they held back in any way. No, the Greeks did well to emerge unscathed from a furious and sustained initial onslaught, one which would have yielded a Liverpool goal had the goalkeeper Dimitri Eleftheropoulos not responded with sublime athleticism to touch over, just, a Steven Gerrard volley from distance.

Olympiakos actually took to the inclement conditions rather well, moving the ball across a slippery, rain-sodden surface to good effect even if in their haste to fashion an early breakthrough they often lost their shape and surrendered their discipline.

This unexpected willingness to attack quite often with a callous disregard for their own well-being at the back - was almost their undoing on countless occasions for Houllier had picked a team capable of mounting spring-heeled counter-attacks.

To this end, Danny Murphy - surprisingly selected ahead of Christian Ziege - was crucial for he, perhaps more than anyone in the Anfield firmament provides tangible evidence that hard work can still carry you a long way in a sport now dominated by prima donnas.

Murphy worked tirelessly and yet, as is so often the case, was a mere spectator when Liverpool's mounting pressure was finally met with its reward on 28 minutes.

It was a nice move, too, Emile Heskey collecting Nick Barmby's astute pass before galloping clear to score with a low drive, his 12th goal in his last dozen games.

Heskey's proficiency left Olympiakos chasing two goals and seemingly uncertain as to whether they should toss all caution to the prevailing wind or rein in their ambition in the hope that their opponents would tire in the evening's final quarter. Olympiakos entertained high hopes until the hour mark when they succumbed for a second time.

This time Barmby was to pull the trigger rather than provide the ammunition, firing in a shot from an acute angle which managed to strike both posts before dropping behind the line.

Liverpool boss Gerard Houllier said afterwards: "I think we deserved it. Over the two legs we've always been in the position to qualify.

"They are a good side who can pass the ball round and move it - we knew that. But we knew we had one foot in the next round.

" Tonight it was a good European game for the fans and the players," he added.

LIVERPOOL: Westerveld; Babbel, Hyypia, Henchoz, Carragher; Barmby, Gerrard (McAllister, 90 mins), Hamann, Murphy (Ziege, 78); Smicer; Heskey.

OLYMPIAKOS: Eleftheropoulos; Mavrogenidis (De Souza, 53), Amanatidis, Anatolakis, Georgatos; Poursanidis, Patsatzoglou, Zetterberg (Niniadis, 63), Djordjevic; Giovanni, Alexandris (Oforiquaye 63).

Referee: M Pereira (Portugal).