Liverpool produced a magnificent performance to reach the Champions League quarter-finals in style.
In a remarkable first half, Real Madrid were torn to shreds by a breathtaking attacking display led by Fernando Torres, their arch-enemy from his Atletico Madrid days.
Torres scored early on, before Steven Gerrard fired home from the spot. And had it not been for an outstanding display from Spanish goalkeeper Iker Casillas, Liverpool would have had a hatful in that first 45 minutes alone.
Gerrard scored a spectacular third seconds after the break to deflate Madrid further and substitute Andrea Dossena added a fourth with three minutes to go.
Sometimes Liverpool can defy logic. So unpredictable in the Premier League of late, their fans were singing about another Rome final long before the end. And who would ever bet against the Anfield men in Europe.
Gerrard struck twice on his 100th European appearance for Liverpool to secure a quite breathtaking victory, Real were humbled for the second time in a fortnight by their old boy Rafael Benitez.
If manager Benitez feels he does not get enough respect for his Champions League achievements at Anfield, this fourth appearance in the last eight in five years will go a long way to gaining him the credit he craves.
England coach Fabio Capello was here for another Benitez masterclass, and Manchester United assistant manager Mike Phelan - Liverpool go to Old Trafford on Saturday - was a more than interested observer.
Anfield was at its European best, a cauldron of pounding sound cascading down from the Kop.
And it inspired a stunning start from Liverpool, with Casillas making two world-class saves in the opening minutes.
Torres, back after an ankle injury, had already embarked on one surging run into the box, before he dumbfounded Fabio Cannavaro with a brilliant turn to control a Gerrard pass, only for Casillas to save with his right foot.
Ryan Babel and Javier Mascherano both had shots deflected wide before Casillas rescued Madrid again, stretching to his left to touch a Mascherano 20-yard effort onto the bar and over.
After 16 minutes Liverpool were ahead. Jamie Carragher's long ball had Real on the turn with Torres and Kirk Kuyt baring down on Pepe.
Torres looked to nudge Pepe from behind, and the Portuguese defender fell, leaving Kuyt to square the ball for Torres to beat Casillas from six yards, only his second goal against Real having managed just one against them for Atletico.
Real were furious with referee Frank De Bleeckere, the official who sent off Marco Materazzi when Inter Milan were beaten at Anfield at this same stage last season. But the Belgian was unmoved.
Pepe was soon booked for dissent before Casillas needed to be at his best to stop a towering Martin Skrtel header, before he somehow beat away a Gerrard shot following more brilliance from Torres on the left.
Gerrard was booked for a foul on Sergio Ramos before more misfortune befell Madrid. A linesman's flag signalled to De Bleeckere after 27 minutes that Gabriel Heinze had handled in the box.
Replays showed the ball hit the former Manchester United man on the shoulder, and he was booked for making his point. But Gerrard was nerveless, driving home the spot-kick.
Real were fuming. Heinze hurled himself feet first into Torres and it needed De Bleeckere and Gerrard to calm the situation, before Jose Reina produced his first saves of the night to turn away a Wesley Sneijder free-kick and hold Raul's header.
Another instinctive save from Reina stopped Sneijder from close range before Mascherano found himself booked after Xabi Alonso had tripped Pepe.
That will rule him out of the next European match, but it was unclear whether the yellow card was mistaken identity or because the ball was kicked away from the free-kick.
Real needed to do something, and they sent on Brazilian forward Marcelo for the anonymous Arjen Robben at the break.
But any plans for a fightback were destroyed just 65 seconds into the second period. Babel got away on the left and laid the ball back for Gerrard to volley superbly high into the net with Casillas helpless.
Real were in pieces, and had it not again been for Casillas - punching the ball away to his right - Gerrard would have had another after 54 minutes.
On the hour Lucas was sent on to replace Alonso, with Saturday's likely epic no doubt in Benitez's mind.
Belatedly Real took off a defender, Cannavaro, and sent on an extra forward in Rafael van der Vaart. But Madrid had been bereft of attacking ideas, and it was far too late by now.
Liverpool were able to indulge themselves by bringing on local teenager Jay Spearing in midfield for Gerrard, an Anfield debut for the former FA Youth Cup-winning captain.
Raul and Fernando Gago both had chances, but Liverpool were cruising at this stage and next to be given a rest was Torres with eight minutes to go, Dossena taking over, only to be booked within seconds.
With three minutes to go, the Italian defender appeared in the box to fire home the fourth goal of the night after a fine build-up involving Babel and Mascherano.