Barcelona's 2-2 draw with Celta Vigo earlier in the evening meant second-placed Madrid could have trimmed their arch rivals' lead to 11 points if they could beat Zaragoza and claim a seventh successive league victory
However, like Barca, they had to settle for just a point with Rodri putting Zaragoza ahead early on before Cristiano Ronaldo levelled things up just before the break with his 28th La Liga goal of the campaign.
Neither side could go on to force a winner in the second half, with Marcelo hitting the post for Madrid and both goalkeepers making a number of vital interventions.
With one eye on Wednesday's Champions League quarter-final first leg visit of Galatasaray, Madrid coach Jose Mourinho opted to shuffle his pack for Saturday night's game, giving starts to the likes of Jose Maria Callejon, Kaka, Luca Modric and Michael Essien.
It was still a formidable-looking Madrid line-up however, and they would not have been expecting to be a goal down after just six minutes.
But that is what happened as Antonio Apono won a midfield challenge with Modric that set Rodri away and the Barcelona youth team product coolly slotted past Diego Lopez.
Zaragoza looked good value for that lead heading towards half-time as they kept Madrid chances down to a minimum, but some poor defending from the hosts allowed Ronaldo to draw the visitors level in the 38th minute.
Two Zaragoza defenders failed to deal with a long pass forward from Pepe and, after Higuain had laid the ball off to Ronaldo outside the area, two more Zaragoza players allowed the Portugal international to bundle through their challenges.
Ronaldo still had to work to do but he managed to drill a low left-footed shot past Roberto Jimenez at his near post.
Roberto will have been disappointed to have been beaten in that fashion, but he kept his side from failing behind immediately after half-time when he denied Ronaldo when one-on-one.
Zaragoza then received a huge slice of luck as Marcelo cracked the loose ball against the post before Essien fired wide.
Roberto was not the only keeper to earn his wages though as Lopez produced two brilliant saves to keep out headers from Helder Postiga in the final 12 minutes as fourth-bottom Zaragoza sought their first league win of 2013.
In between those saves Marcelo got into a good position but opted for a cross instead of shot, and drilled the ball in front of his team-mates, while Ronaldo had one late chance to snatch all three points for Madrid but saw his 90th-minute strike saved.