Malaga banged in two goals in the first half and two in the second in a dominant display.
Ignacio Camacho, Joaquín, Javier Saviola and Roque Santa Cruz all scored for Malaga.
Saviola was on the pitch for 62 minutes against Granada. He scored in the 33rd minute, assisted Joaquín's goal in the 26th minute and took three shots.
Malaga now sit in fourth in the table with a record of seven wins, four losses and four draws.
At 18th in the table, Granada are currently fighting for survival and remain one point adrift of safety with three wins, nine losses and three draws.
Malaga maintained control of the ball for 53.4% of the contest of the match, a testament to their movement and linking play in the open field.
Malaga got off 11 shots, including nine on goal, during the match, a direct result of their 54 duels and 13 headers won.
The most effective of Malaga's three substitutions was Santa Cruz, who, after replacing Saviola in the 62nd minute, scored one goal and took two shots.
Willy Caballero pitched in with eight stops.
The combination of Portillo to Jesús Gámez was the most common during the match, as the two players connected 14 times.
Granada had 46.6% of the possession during the loss.
Granada had 22 shots, including eight on target.
Gabriel Torje had seven shots for Granada, more than any of his team-mates.
Iriney's 13 passes to Mikel Rico were the most of any Granada team-mates during the match.