Gonzalo Higuain and Angel Di Maria put the hosts in a commanding position with a goal apiece in a two-minute spell midway through the first half but Zaragoza were unfortunate not to get back into the game early in the second period as Jose Mari fired a shot off the crossbar and Helder Postiga had a goal wrongly ruled out for offside.
Real coach Jose Mourinho said afterwards: "I didn't enjoy the match very much, we can and must play better. The important thing is to win and do it calmly, but we have to play better than we did.
"In the past two seasons if Alonso and Khedira were missing we were desperate. Today, without them, the team has played, won and did enough to win."