Champions Barca host unbeaten leaders Real Madrid at the Nou Camp on Monday and third-placed Villarreal seized their chance to cut the advantage held by the big two before the eagerly-anticipated "Clasico".
Zaragoza, who sacked coach Jose Aurelio Gay on November 18 and gave former Mexico boss Javier Aguirre the task of avoiding relegation, remain rooted to the bottom with just eight points from 13 matches.
Pablo Osvaldo's superb volley gave Espanyol a 3-2 win at Atletico Madrid that cemented the Barcelona-based club's hold on fourth, two points behind Villarreal, while Sevilla squandered the lead and lost 3-1 at home to Getafe and stay in seventh.
Cazorla added a second nine minutes later with a clever lob and Brazilian Nilmar put the game beyond Zaragoza's reach with a neat finish in the 65th.
Zaragoza defender Matteo Contini was dismissed moments before Nilmar's goal after picking up a second yellow card.
"We need to do a huge amount of work," Aguirre, who struck the dugout in frustration after Villarreal's third goal, told a news conference.
"We have not had much time yet to work... but the reality is that we have only taken a point from two matches (since I took charge)."
Atletico keeper David De Gea got hands to Osvaldo's powerful volley with just over 10 minutes left but could only divert the ball up and into the net.
A first-time effort from Getafe striker Miku crashed back off Andres Palop's crossbar just after the break before Manu del Moral beat the Sevilla goalkeeper from the penalty spot in the 57th and Miku added a second three minutes later.
