The Portuguese forward restored parity with a precise finish but they could not find a winner, letting Barcelona off the hook for their earlier slip-up in Vigo
On-loan Barcelona B player Rodri gave the hosts the perfect start as los Merengues struggled to get a foothold in the game. Cristiano Ronaldo managed to net an equaliser before the break with his 28th league strike of the season but they could not find another in a lacklustre second.
Things did not go to plan from the start for Jose Mourinho's men as the relegation-embroiled side took a surprise lead in the sixth minute.
Apono poked the ball off the toe of Luka Modric and straight into the path of Rodri who raced through one-on-one with Diego Lopez. He shaped to hit the ball across the keeper but stylishly placed it in the other corner, finishing with aplomb.
Madrid were extremely rushed in possession but still came desperately close to finding an equaliser soon after. Marcelo's cross-field pass fell over the shoulder of Ronaldo but he was unable to guide his first-time volley into the top corner.
Los Blancos were struggling for fluency in the final third and a searing Rodri effort that arrowed narrowly over the bar almost doubled their woes.
But the visitors were presented with an opportunity to draw level with 27 minutes on the clock as Roberto Jimenez failed to collect Luka Modric's in-swinging free kick. Glenn Loovens' sliced clearance presented Pepe with a chance to head in the equaliser, but the Dutchman recovered to poke the ball off the line.
Madrid were resorting to a long-ball game but it paid dividends in the 38th minute. Pepe's pass from deep was not dealt with by Loovens and Ronaldo bulldozed through the defence before lashing a low shot past Roberto at his near post.
The scoreline would have been completely reversed two minutes later had it not been for a top save from Roberto to keep Michael Essien's header out of the net.
The reigning Liga champions did not let up after the break but the score somehow remained level as Marcelo hit the post of an open goal after Roberto had done superbly to deny Ronaldo in the 48th minute.
Zaragoza were by no means ready to surrender and they soon returned to the intensity levels that had caused the visitors so many problems in the first half.
In an attempt to revive his team Mourinho added Sami Khedira, Angel Di Maria and Mesut Ozil on the hour mark, but the game remained delicately balanced.
In fact it was the Blanquillos who were looked increasingly likely to steal a winner but Lopez ensured the draw as he did brilliantly to keep out a pair of top-drawer headers from Helder Postiga in the closing stages.
The result means Madrid remain 13 points behind Barcelona, who could only manage a 2-2 draw with Celta Vigo earlier on Saturday. Zaragoza, meanwhile, will be hopeful that the unexpected result can provide a late surge to safety.