The win means that Barcelona stretch their lead at the top of La Liga to 16 points with Real Madrid still to play this evening.
A much-changed Barca side without the likes of Lionel Messi and Andres Iniesta started the game quite slowly as Zaragoza were able to put their defence under pressure through Helder Postiga and the on-loan Blaugrana man Rodri.
The away team finally managed a counter-attack on 12 minutes but Xavi was crowded out on the edge of the box after Tello's cut-back.
Barca started to dominate after the opening goal and shortly before half time they got their second as Thiago again played a big part. The midfielder cleverly slipped the ball through to Tello who sent Roberto the wrong way and fired in at the near post.
Two minutes into the second period it could have been three. Thiago released Sanchez, who ran the length of the Zaragoza half before chipping the ball over the goalkeeper, only the see it bounce back off the crossbar.
They didn't have to wait long for another goal, though. Tello ran clear on the left, beating Glenn Loovens, before opening his body and curling the ball in the bottom corner.
The visitors were comfortable after that and apart from a couple of half-chances, were happy to see out the game with a three-goal lead.