Granada started the stronger side and their pressure forced a series of corners but the visitors could not make any of them pay.
Before the break it was 2-0, Javier Saviola scoring after being put through by Julio Baptista.
Torje continued to toil for the away side but another effort went wayward before Granada were inches away from a goal back when Odion Jude Ighalo struck the post.
However, Malaga made the points secure in the 75th minute when Ignacio Camacho headed in a cross from Joaquin.
It was 4-0 with five minutes left to play courtesy of substitute Roque Santa Cruz.
Fabian Orellana almost snatched a late consolation goal for Granada but his effort came back off the crossbar.