They took the lead after 18 minutes when Javier Saviola finished off a sweeping move, with that score still standing at the interval.
Both sides had chances in the second period, but neither could find the back of the net as Bilbao's struggles continued.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
MALAGA: Caballero; Lugano, Weligton, Antunes, Sanchez; Baptista, Camacho, Isco, Portillo; Saviola, Piazon
BILBAO: Raul; Iraola, Aurtenetxe, Laporte, Gurpegi; Susaeta, Iturraspe, Herrera; Aduriz, De Marcos, Ibai