A mistake by Barcelona defender Dani Alves in the eighth minute allowed Juanmi to fire Malaga in to the lead, a lead they maintained relatively comfortably.
The defeat left them in second place just a point behind behind Real but with their Madrid rivals still to play its one game in hand.
Much of the talk before this weekend's round of fixtures surrounded the effectiveness of MSN versus BBC; acronyms for the players that have been pivotal in attack for Barcelona and Real Madrid this season.
Messi, Suarez and Neymar for the former; Benzema, Bale and Cristiano Ronaldo for the latter.
Up until the start of the year, Real Madrid's strike force had dominated. But since the start of 2015 Barcelona's new look triumvirate has thrived.
Lionel Messi has scored 14 goals alone, two more than the entire Real strike force, whilst Neymar has bagged ten goals, and Suarez four.
But the three players were surprisingly subdued and had no answer to Malaga's resolute defending.
"We're used to these kind of games. I'd like it to be an accident but it is becoming habit, the opposition close up and we can't find a way through," Barcelona boss Luis Enrique told AFP after the game.
"These kind of results are sometimes a good reminder that other sides have their qualities. You could consider this a deserved defeat."
The result ended a superb run of form for Barcelona, who had won their last 11 matches in all competitions and scored 42 goals in the process.
"They scored and shut up shop," added a frustrated Sergio Busquets.
"They let us use the ball out wide and we tried, but the final ball wasn't there and we didn't create clear cut chances."
Real Madrid can go four points clear of Barcelona on Sunday when they play Elche.