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.
Barcelona made seven changes from the side who progressed to the semi-finals of the Champions League this week.
Out went Lionel Messi, with his hamstring not risked against Real, Andres Iniesta, Sergio Busquets and Jordi Alba, while Gerard Pique, Pedro and David Villa both dropped to the bench.
In came Marc Bartra, Martin Montoya, Alex Song, Thiago, Alexis Sanchez, Cesc Fabregas and Tello.
Zaragoza who have not picked up a win since mid-December, made three changes from the side who lost at Deportivo La Coruna, with Edu Oriol, Christian Romaric and the suspended Abraham all missing out.
Tello fired a warning to the Zaragoza back-line after 16 minutes when he shot over from 20 yards and three minutes later the visitors were ahead when Thiago found the bottom left-hand corner from just inside the area.
Helder Postiga had the chance to register the home side's first decent effort on goal after 25 minutes, but from 18 yards out he mishit his effort.
Barcelona were more ruthless and six minutes before the break they were two up. Tello combined brilliantly with Thiago to open up the Zaragoza defence before placing a curling effort past Roberto and into the bottom corner.
The home side brought on Antonio Apono and Jorge Orti for Martin Jose Mari and Victor Rodriguez respectively, but the switches did little to change their fortunes.
Barcelona started the second half almost as strongly as they had finished the first with Alexis Sanchez hitting the bar after 46 minutes with a lobbed effort from 18 yards.
After just 53 minutes they were three up when Tello cut in from the left and, after easing past Apono, he fired across Roberto and into the net.
Roberto was called into action once more in the 69th minute, tipping over Tello's lob and then catching Fabregas' shot from the following corner.
Apono and then fellow sub Ruben Rochina shot over for Zaragoza, before Paco Montanes somehow managed to miss the target from six yards, with his effort summing up Real's evening.