Helder Postiga headed the visitors in front from Victor Rodriguez's free-kick after just three minutes and the latter then added a second 25 minutes later with a simple finish from Abraham's cross.
Granada seemed dead and buried when Iriney was shown a straight red card for bringing down Apono midway through the second period, but they did manage to get a goal back with just over 10 minutes remaining when Youssef El-Arabi headed home from Fabian Orellana's corner.
And they should have equalised with virtually the last attack of the game when Inigo Lopez somehow failed to connect with Mikel Rico's cross.
Granada came into the game off the back of consecutive victories, but any chance of three in a row were dashed by a lacklustre first-half performance lacking in conviction at both ends of the field.
Postiga rescued a 1-1 draw for Portugal against Northern Ireland in midweek and he continued his scoring form early on as he was given a huge amount of space to head home Victor's free-kick.
The early goal seemed to settle Zaragoza into a rhythm they have rarely showed so far this season and more slack defending from Granada allowed them to double their advantage midway through the half as Abraham's low cross was swept home by Victor.
Things could have been even worse for the hosts before half-time as Franco Zuculini's acrobatic header flew wide and Tono made a smart stop to deny Paco Montanes, but they nearly had a way back into the game straight after the break as Lopez headed just over from Gabriel Torje's cross.
The game seemed completely over as a contest when Iriney was shown a straight red card after chopping down Apono just before he could break into the area with 18 minutes remaining.
But within five minutes the hosts' had reduced the arrears as El-Arabi rose highest to head home Orellana's corner.
Postiga should then have sealed the points, but he blazed wildly over after rounding Tono.
That miss gave the hosts hope and they very nearly equalised in stoppage time as Lopez ghosted into the box unmarked but could not find the connection needed to beat Roberto from close range.