Real, who have not won at home in the league since August and sacked their coach John Toshack last month, had not conceded five at home since February 1974, when a Johan Cruyff-led Barcelona thrashed them 5-0.
"This defeat was a great affront to every Madrid supporter," said Real's new coach, Vicente Del Bosque. "We did not play like a team and the defence collectively had serious problems. We have to forget personal issues and play like a team."
Hovever, he denied that he was contemplating resigning, despite two defeats and a draw in his first three league games and the fact that his is only an interim appointment until the end of the season. Del Bosque insisted: "I not going to throw in the towel. I have the courage and enough character to weather this storm and intend to get over this situation."
The rout started on 29 minutes when Savo Milosevic found himself unmarked and headed past the helpless Albano Bizarri in the Madrid goal. Juanele added two more goals before half-time as Real left huge gaps in defence.
Raul raised hopes of a Madrid fightback when his shot from the edge of the area was mishandled by Zaragoza's goalkeeper Juanmi Garcia and spun into the net after 53 minutes. However, that was to prove the only piece of luck for the home side.
Ander Garitano added his name to the list of Zaragoza scorers a minute later when Ivan Helguera failed to cover back properly. Milosevic scored Zaragoza's fifth after 68 minutes, with Helguera again at fault. It was the the former Aston Villa striker's 15th goal of the season and made him the league's top marksman.
Barcelona finally broke their four-game losing streak with a 3-2 home win over struggling Oviedo. The Catalan club had the game well under their control with three goals in the first 27 minutes, the first two coming from Philip Cocu and third from fellow Dutchman Patrick Kluivert, who scored after connecting with a Luis Figo cross.
However, Barcelona relaxed in the second half and allowed Oviedo to creep back with late goals from Roberto Losada and Juan Gonzalez.
In Italy, Christian Vieri scored his first league goal since September as Internazionale continued to make light of the absence of the injured Ronaldo with a 3-0 win over Udinese at San Siro. Alvaro Recoba, with his third goal in three matches, hit the first; the 18-year-old debutant Nello Russo added a last-minute third
Hernan Crespo scored twice in Parma's 4-1 victory over Torino, making him Serie A's top scorer with nine goals and equalling the club record of 49 goals set by Gianfranco Zola, now with Chelsea.