Kike Sola put the hosts ahead on 28 minutes and Nino doubled the lead 15 minutes into the second half, leaving an impotent Deportivo with too much to do in the remaining half an hour.
The Galicians were second best for most of the game but came into life in the final 20 minutes, and a goal by Javier Camunas in the first minute of stoppage time made for a tense finish. However, Jose Luis Mendilibar's side held on for the three points.
Three players limped from the field in a scrappy game in which both sides struggled to create chances in difficult conditions.
Forit was a second consecutive home win that moves them into 10th place in the Primera Division table with a haul of 28 points, while Zaragoza remain in 13th place and only four points clear of the relegation zone.