Zaragoza came into the match having taken just 27 points from 30 matches and occupying 18th place.
And their performance replicated their standing as Tito Vilanova's team - 13 points clear of second-placed Real Madrid - dominated from the off.
Thiago Alcantara struck the opener on 20 minutes before Tello stepped in with his brace.
Barca No2 Jordi Roura said: "The result is excellent! La Liga is basic, it’s our number one objective. The players that played today aren’t our usual starters, and they’ve been helping us out for weeks now. We were a great team today.
"It has been a long week but we weren’t thinking about reserving players today. We selected the players that we simply thought were in the best condition to play."