Somehow, Rafael Benitez produced a game plan and a streak of sheer defiance in his erratic team to leave Juventus on their knees and out of Europe in front of their own disbelieving supporters.
The Reds now meet Chelsea in a two-legged semi-final on April 27 and May 3, with the second leg at Anfield.
The red heroes were all the unsung defenders; Jamie Carragher, Sami Hyypia, Djimi Traore and Steve Finnan, plus the toil of John Arne Riise and the clever, inventive play of Xabi Alonso.
There was no Steven Gerrard, out with a groin injury at the worst possible moment as far as Benitez was concerned.
And, as expected, Spanish midfielder Xabi Alonso returned to the side for the first time since New Year's Day as his replacement.
Milan Baros was also back up front with Hyypia in defence, while Jerzy Dudek's experience was finally preferred to 19-year-old Scott Carson in goal.
But the backdrop of the bitter memories of Heysel were immediately obvious.
The noise of police helicopters and the whistling of Juve's fans hung over this vast concrete bowl of a stadium.
Liverpool's fans had been taken from the airport before the game to out-of-town restaurants and bars before being bussed straight into the stadium in an attempt to keep both sets of supporters apart as the Turin public honoured the memory of the 39 fans who died 20 years ago at Heysel.
Banners draped from the Ultras end said: "39 angels are with us tonight" and "What is deep in the heart never dies".
But sadly, although a vast empty area had been left around the Liverpool fans, missiles were being exchanged before the match.
It is hard to know who started it, but objects were clearly being thrown from both sets of fans and the pitiful amount of stewards one thin line of yellow were doing nothing to stop it.
Liverpool's fans retreated back up the terraces and under cover, but the incident left a bad taste in the mouth and it took an age for the police to move into an area between the rival fans.
Order had been restored when the game finally started and Juventus should have been level on aggregate when Zlatan Ibrahimovic met a left-wing cross just six yards out and hoisted his effort over the crossbar.
Liverpool defended in depth, but Alonso was still able to find yards of space to link defence with attack.
The former Real Sociedad star created Liverpool's best first-half chance when he fed the ball into Luis Garcia's path, but Gianluigi Buffon was swiftly off his line to snatch possession from the little Spaniard's feet.
Pavel Nedved and Alessandro del Piero threatened to evade Liverpool's offside trap, but the Anfield men stood firm and Alonso got himself booked for dissent, his long-running arguments with referee Valentin Ivanov finally causing the Russian to lose his patience.
Luis Garcia and Baros both almost caught the home defence cold with interceptions.
But there was little for the front pair to work with, so much were Liverpool on the defensive.
Juventus brought on an extra striker in Marcelo Zalayeta for Ruben Olivera at the break and went for a 4-3-3 formation.
But it was Liverpool who should have been ahead early in the second half, a priceless moment that they had been praying for as they defended with their lives.
The ball that created the opening was a peach of a pass from Alonso to Baros in a couple of yards of space. He held off Paolo Montero as he forced his way into the area but his shot slipped inches wide of the far post.
On the hour, Vladimir Smicer took over from Antonio Nunez, a gamble from Benitez as he looked for that one piece of attacking flair that would make all the difference.
Ibrahimovic was booked for flattening Hyypia, the Juventus frustrations now becoming clear as they fought for the goal that would surely see them through.
It almost came when Nedved's header from a Mauro Camoranesi free-kick was saved by Dudek. Del Piero was next into the book following an exchange with Smicer.
Djibril Cisse came on for his first match since breaking his leg in October, replacing Baros, before Biscan headed over from an Alonso free-kick.
Juve were now being whistled by their fans, before Fabio Capello threw on Gianluca Pessotto and Stephen Appiah for Cannavaro and Camoranesi, searching for inspiration and fresh legs. Luis Garcia was then replaced by Anthony Le Tallec with five minutes left.
But Liverpool fought like tigers and erupted in joy at the final whistle, with an all-English semi-final to look forward to.