The home side quickly went ahead when Helder Postiga won a penalty in the fifth minute that was converted by Apono, and Postiga added a second on his own just after the half-hour mark.
Los Che pulled one back through Jonas just four minutes later, and the same player found the net again to equalise in the 69th minute.
Real Zaragoza suffered a setback when Leo Franco was given a red card in the 77th minute, but they held on for the draw.
Los Blanquillos had possession for a mere 37.0% of the contest.
Real Zaragoza had 14 shots, including six on target.
The six attempts by Rubén Rochina were the most of any Real Zaragoza player.
Apoño went off due to injury in the 45th minute and was replaced by Stefan Babovic.
Valencia enjoyed possession of the ball for 63.0% of the contest.
Xotos had 11 shots, including eight on target.
Daniel Parejo had three shots for Valencia, more than any of his team-mates.
Jeremy Mathieu was brought on to replace Ricardo Costa in the 65th minute when the latter went down with an injury.