Odion Ighalo struck a post for Granada and Antonio Tono made a fine save to deny Zaragoza's Cristian Sapunaru, but the honours were even at full-time, leaving Zaragoza two points clear of the drop zone and Granada one point better off.
The game began brightly with early chances for both sides, but as the contest wore on the shutters came down with neither team willing to risk defeat against a direct rival.
Gabriel Torje crashed a shot over the bar just seconds into the game and soon after Ighalo headed narrowly wide, while at the other end Ruben Rochina was off target for Zaragoza before Tono got a first to Victor Rodriguez's free-kick,
Ighalo found the upright in the 19th minute, getting up to head Nolito's corner desperately close to the target.
At the other end, Rochina twice tried his luck from 25 yards but with little success, missing twice before Granada's Diego Mainz headed wide from another Nolito corner.
As the second half began, Rochina was still being tempted into long-range efforts but with no more success.
However, it was his 65th-minute free-kick that found Sapunaru for Zaragoza's best chance, Tono making a brilliant save to tip it over the crossbar.
Diego Buoanotte was presented with a good opportunity for Granada but mis-hit his shot to give an easy save to Leo Franco in the 73rd minute.
Soon after, Tono fumbled Stefan Babovic's shot but did enough to keep it out, but the contest petered out, with a poor effort from Ighalo dribbling wide in the only thing approaching a clear chance in the final 15 minutes.