Neil Mellor put them into a 2-1 lead in the 80th minute. He had only just come on but was in position to slam the ball home after Antonis Nikopolidis palmed an Antonio Nunez header to him. It was almost inevitable that the overwhelming Steven Gerrard, with three minutes remaining, should drill the decisive goal. With that lash of his right boot, this was once more an arena of marvels.
Hours before kick-off there were packs of Olympiakos fans taking photographs near the Shankly Gates. They had come to pay their respects and for much of the world this is still a football shrine, but the professionals usually treat it as just another halt on the endless circuit of their careers.
The place might not even have enough of an aura to prevent Gerrard from leaving, but for the time being it is the captain who is the spirit of the place. When he claims that he want to see success at the club, the midfielder is not implying that he intends to be a surly onlooker in the months ahead.
Liverpool wanted to play in a direct, high-tempo fashion but it could only work because Gerrard offers both the energy and the accuracy. By the second minute, he was already sweeping over his third corner-kick. Milan Baros claimed his header had crossed the line before Anastasios Pantos cleared, but the referee Manuel Mejuto Gonzalez had spotted a push by the Czech striker.
It appeared that it would only be a matter of time before Liverpool not only made a breakthrough but smashed the visitors to rubble. Olympiakos usually lay shoddy foundations in English soil and had lost all five previous European matches in this country without recording a goal.
Then again, they had never come here with Rivaldo in their ranks. The Brazilian has waned since winning the World Cup in 2002, when Liverpool attempted to sign him. He ran sparingly but also did so with discrimination.
After 27 minutes, he broke away from Xabi Alonso and was halted only by Sami Hyypia's foul. The midfielder took the free-kick himself and with Nunez breaking out of the defensive wall his shot flew through the gap and past an unsighted Chris Kirkland.
Liverpool were in trouble. They had menaced with their early barrage of corners, but it was the Greek set-pieces that had become genuinely ominous. On the verge of half-time Jamie Carragher brought down Rivaldo, but as the crowd winced in mass premonition the Brazilian made a mistake.
He lay on the turf long enough for a physio to be called and then had to leave the field. He could not be allowed back into the action until play had resumed. So it was that Predrag Djordjevic, a less gifted understudy, fired the ball straight to Chris Kirkland's arms.
Liverpool needed far more than a reprieve. While Baros was back after three weeks out with a hamstring injury, the side had no other authentic striker. So it was that the approach work had plenty of zest but never got close enough to the Olympiakos goalmouth.
Rafael Benítez's alterations at the interval were inevitable as he brought on Florent Sinama-Pongolle, at the expense of Djimi Traoré, to partner Baros. This had the valuable side effect of shoving Harry Kewell back to his best position, on the left flank.
Two minutes after the restart, the Australian pulled back the low cross that Sinama-Pongolle turned into the net. Liverpool's target looked achievable once more and when Gerrard picked up the yellow card that will bring him a suspension there was no means of telling whether he would serve it in the Champions League or the backwaters of the Uefa Cup.
Rivaldo was still stirring faint memories, though, of his dis play for Barcelona in a 3-1 win at Anfield in 2001. Luckily, he lacked the speed to run through on goal in the 59th minute and made do with thrashing a 20-yarder well wide.
Three minutes later, Gerrard's sense of direction was more acute and his snap shot found the net because of faulty handling by Nikopolidis. Once again, though, Mejuto Gonzalez noted a prior foul by Baros, with Gabriel Schurrer the victim. Liverpool, with their lack of firepower, could not afford such decisions.