The champions were missing the injured Lionel Messi and struggled to find a way through the home defence until fullback Adriano cut in from the right and curled a powerful shot into the far corner moments before halftime.
Barca defender Gerard Pique diverted the ball onto the crossbar with his back in the 58th minute before Malaga came desperately close to an equaliser.
Roque Santa Cruz found space on the left and cut the ball back from the byline but teenage forward Fabrice Olinga scuffed his shot and it bounced away off a post.
Barca's new signing Neymar looked sharp when he came off the bench with around half an hour left and the Brazil forward drew a fine save from goalkeeper Willy Caballero with a free kick.
Caballero's opposite number Victor Valdes then rescued his team with a superb point-blank save from substitute Seba Fernandez's header and a deflected Neymar shot flew narrowly over in a frantic finale.
The victory leaves Barca at the top of the standings after two matches following their 7-0 drubbing of Levante in last weekend's opening game.
Atletico Madrid also have six points in second after Turkey playmaker Arda Turan produced a masterclass to help them to a 5-0 drubbing of city rivals Rayo Vallecano in the earlier kickoff at the Calderon.
(Editing by John Mehaffey)
