Barca's priority is to conserve their energies for the Champions League semi-final against Bayern Munich in two weeks time and players such as Lionel Messi, Andres Iniesta and Gerard Pique were all missing.
Making the most of their opportunities were Barca youth academy products Tello and Thiago Alcantara who scored the goals as the leaders moved on to 81 points with seven games left to play.
Champions Real Madrid, in second, cut the deficit back to 13 again with a 3-0 victory at Athletic Bilbao in the late game.
Thiago ran the length of the pitch on a counter-attack and fired in off the far post after a one-two with Alexis Sanchez in the 20th minute. The Spanish international then laid on the second for Tello.
His through ball put the left winger clear to lift his shot over Roberto just before halftime, and Tello sped past his marker to squeeze the third inside the far post in the 53rd minute.
Alexis had already hit the crossbar but Zaragoza, who have yet to win in 2013, rarely threatened.
"We miss Messi, obviously, but we have some great players with a lot of football in their boots," Thiago told Spanish broadcaster Canal Plus.
"We would like to win the league as soon as possible but there are still many games left to play. The title isn't won yet."