An early goal from Helder Postiga put Zaragoza ahead, the Portugal striker burying a close-range header.
Victor Rodriguez added a second for the visitors when he unleashed a right-foot drive in the 27th minute.
A header by Youssef El-Arabi in the 77th minute pulled one back for the hosts, who were hamstrung by a straight red card for Iriney five minutes earlier.
Granada CF are in 16th place with a record of two wins, four losses and two draws.
Los Blanquillos now sit in 15th in the table with a record of three wins, five losses and zero draws.
Los Manos had 49.1% of possession during the victory. The winners had 14 shots, including five on target.
Granada CF attempted three shots, including three on target.
Granada CF and Real Zaragoza evenly split the possession during the first half, but Real Zaragoza took a 2-0 lead into the dressing room.