Barcelona fans celebrated long into the morning after the stunning victory at the Bernabeu Stadium gave Barca a seven-point lead with four matches left.
What made the result so remarkable was that it came four days after Barca's disappointing 0-0 tie at home against Chelsea in the Champions League.
Thierry Henry and Lionel Messi scored two goals apiece for Barcelona, which has scored 100 goals in 34 league matches, only seven short of the record set by Real in 1989-90.
"The best Barca team of all time was on display yesterday and led Madrid a merry dance it will never forget," said Madrid daily El Pais.
It went on to say that Real Madrid was "like putty in their hands."
While the Madrid press lamented the Merengues' performance -- Marca called the evening a "scandalous goalfest" -- the Catalan sports newspapers were delirious.
"Goalfest, Humiliation and Champions!" was the headline in Sport. "This time the good guys won," said El Mundo Deportivo columnist Fernando Polo.
Barcelona is now off to London for its return game against Chelsea on Wednesday.
"It is certainly not going to hurt," Barca coach Pep Guardiola said. "It's going to put us in very good shape. We are going there to seal our place in the final."
May 2 in Madrid
Real Madrid 2 Barcelona 6. Goals: Higuain 15, Sergio Ramos 56; Henry 18, 58, Puyol 20, Messi 36, 75, Pique 83.
Real Madrid --Casillas, Sergio Ramos, Cannavaro, Metzelder, Heinze, Robben (Garcia, 79), Diarra, Gago, Marcelo (Huntelaar 60m), Raul, Higuain.
Barcelona --Valdes, Dani Alves, Puyol, Pique, Abidal, Xavi, Toure (Busquets, 85), Iniesta (Bojan, 85), Messi, Eto'o, Henry (Keita, 61).
Referee:Alberto Undiano Mallenco.