The match was a dress rehersal for next week's Copa del Rey final between the two teams in Barcelona, and Zaragoza served notice that they should not be underestimated by the reigning Spanish champions.
Real, who started without the injured Raul and Ronaldo and opted to rest Ivan Helguera and Luis Figo, were a shadow of their normal selves and looked sluggish after their midweek UEFA Champions League endeavours.
The hosts did move ahead shortly before the half hour mark courtesy of a strike from Ronaldo's deputy for the night Javier Portillo, who neatly headed home from Juanfran's pinpoint right-wing cross.
However, Zaragoza were full value for their equaliser which arrived just five minutes later.
Paraguayan defender Delio Toledo (pictured) was the man who breached Real's defence climbing to head home from a left-flank corner to net his first goal of the campaign.
Los Merengues attempted to step up the pace after the break and introduced Guti and Figo into the fray on the hour mark, but could not break down Zaragoza's well-organised backline.
The point edges Zaragoza further away from the relegation zone, while Real extend their lead at the top to seven points ahead of Sunday's programme.
Real's cross-town rivals Atletico Madrid suffered a blow in their pursuit of a European place as they fell to a 2-1 defeat at Real Sociedad.
The Basque outfit moved ahead ten minutes before the break when Russian midfielder Valery Karpin converted from the penalty spot after a foul by Atletico defender Matias Lequi.
The hosts doubled their advantage seven minutes later when Diego Simeone put through his own net.
Atletico improved after the break and reduced the arrears thanks to a fine strike from substitute Veljko Paunovic with 20 minutes remaining but, despite late pressure, could not find an equaliser.
The success moves Sociedad into 12th spot while Atletico remain fifth.
Match summaries:
Real Madrid 1-1 Real Zaragoza
Real Sociedad 2-1 Atletico Madrid
