Joaquin Sanchez scored in the 26th after defender Pape Diakhate had slipped, letting the Malaga forward take Javier Saviola’s pass and slot under goalkeeper Antonio ”Tono” Rodriguez.
After teammate Jesus Gamez had hit the goal-frame, Saviola doubled Malaga’s advantage in the 33rd with a great individual effort, cutting back to gain a wider angle before firing in with a right-footed shot.
Granada’s Odion Ighalo hit the upright before Ignacio Camacho and Roque Santa Cruz scored for Malaga in the 75th and 86th minutes.
Malaga is level on points with Real Betis, which hosts league leader Barcelona on Sunday. Granada is winless in four games and one point from safety in 17th place.
Earlier, Real Sociedad defender Carlos Martinez scored an injury-time equalizer to secure a 1-1 home draw with Getafe.
After an attractive second half with chances for both teams at Anoeta stadium, Getafe was moments away from a fourth straight victory when forward Angel Lafita charged into the area to head home Jaime Gavilan’s cross in the 86th.
But Martinez was left unmarked to meet Alberto de la Bella’s lobbed pass at the far post and head the ball into the net in stoppage time to split the points.
”It was a free-flowing game, but the goals were hard to come by,” said Martinez. ”We had to settle for the point.”
Sociedad remained undefeated in five rounds and moved up into eighth place, two spots behind Getafe in sixth.
Real Madrid visits Valladolid later before Valencia plays Osasuna.
Also on Sunday, second-place Atletico Madrid hosts last-place Deportivo La Coruna. Levante hosts Mallorca, and Celta Vigo is at Athletic Bilbao. Rayo Vallecano plays Real Zaragoza on Monday.