The visiting Andalusians had a couple of chances to score through Odion Ighalo, but there was little else to separate the sides in a contest short on inspiration and littered with misplaced passes.
Granada stayed 16th on 27 points with 11 games left in the season.
Zaragoaza, yet to win in 2013, are 17th with 26 points, two ahead of the relegation places and 18th-placed Real Mallorca who beat Sevilla 2-1 on Saturday.
Promoted Galician sides Celta Vigo and Deportivo La Coruna occupy 19th and 20th places with 23 and 17 points respectively after defeats this weekend.
Los Maños controlled the ball for about half the match.
Real Zaragoza had eight shots, including three on target.
Rubén Rochina had five shots for Los Blanquillos, more than any of his team-mates.
Offside was called against Granada eight times during play.
The four attempts by Odion Ighalo were the most of any Granada player.
Toño stopped four shots.
Guillherme Siqueira's 16 passes to Nolito were the most between Granada team-mates during the match.