Bernd Schuster's side beat Real Betis away last weekend to climb five points clear of the relegation zone and they made it welcome back-to-back wins on Sunday, with a first-half brace from Nacho Camacho setting them on their way to a 4-1 triumph.
Youssef El Arabi missed a penalty moments before the break that would have given Granada hope, and Malaga capitalised with a third from Nordin Amrabat before Juanmi completed the rout.
El Arabi made amends for his earlier miss by netting 12 minutes from the end, but it was scant consolation.
The hosts jumped into a 15th-minute lead when Samu crossed from the left and Camacho was on hand to guide a header into the right corner.
With 36 minutes the lead was doubled, the head of Camacho again doing the damage as he rose to meet Pablo Perez's corner with a firm effort high into the net.
Granada were offered a way back in the 43rd minute when Samu brought down Yacine Brahimi in the area, but El Arabi saw his spot-kick saved by Willy Caballero.
The hosts won a penalty of their own four minutes after the restart when Jeison Murillo fouled Camacho in the box, Amrabat succeeding where El Arabi had earlier failed with a confident finish into the right corner.
Juanmi's close-range finish from Jesus Gamez's cross made it four in the 74th minute, while Granada salvaged a slither of pride when El Arabi thumped home from the edge of the box minutes later.