© Getty Images
David Strettle got the home side off the mark just four minutes into the game as the Aviva Premiership team added four tries in the first half.
Duncan Taylor added a brace in the second period as Saracens continued to dominate, finishing the game with nine tries.
Owen Farrell put in a strong performance with the boot, converting eight of the nine tries and adding a penalty.
The result leaves Saracens five points clear at the top of pool three, while Zebre remain bottom.