Barca coasted to a 7-0 win in their opener aganist Levante last weekend, but they were made to sweat at La Rosaleda.
Adriano grabbed victory with a memorable 25-yard strike just before half-time although the hosts almost equalised after the break when Fabrice shot against the post from close range.
Barca were without their injured playmaker Lionel Messi and the best they managed early on were a couple of tame headers from Alex Song and Cesc Fabregas.
Malaga goalkeeper Willy Caballero then held on when Andres Iniesta shot from the edge of the area.
Victor Valdes tipped a Vitorino Antunes free-kick around the post before Barca took the lead moments before the break.
Adriano blasted a shot from 25 yards that caught the otherwise impressive Caballero slightly flat-footed as it flew across him and into the corner.
Adriano was forced off by injury shortly after half-time before another defender, Gerard Pique, almost made it 2-0.
The Spain international ran on to Xavi's free-kick before looping the ball against the crossbar with the back of his head.
Malaga had their chances to level the game with none better than Fabrice's 68th-minute effort.
Roque Santa Cruz set him up after dribbling past Valdes and pulling the ball back to the top of the six-yard box, and while the young forward kept his cool, his shot hit the base of the post.
Malaga had one last chance when Jesus Gamez picked out Sebastian Fernandez but his free header was blocked by Valdes, who then had to remain alert to keep out Fernando Tissone's follow-up to ensure the points.