Sevilla moved level with the Catalans on 13 points at the top of the table with a 1-0 win over Real Sociedad thanks to on-loan Barca winger Gerard Deulofeu's winner, whilst Atletico Madrid are now just two points behind the leaders as they too won 1-0 away at Almeria.
Barca stretched their run without conceding a goal to six games yesterday, but lacked the spark they have shown so far this season as Lionel Messi was kept in check by the Malaga defence.
"We weren't precise in the last few metres of the pitch, but at no point did we suffer," said Barca boss Luis Enrique.
"It was the most difficult game for us so far, but that was down to what our opponents did right.
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"We didn't play as well as we can and we just have to continue improving and correcting things."
In a first-half of few chances Nordin Amrabat had the only shot on target as his low effort was easily held by Bravo.
The visitors were similarly short of ideas in the second period provoking coach Luis Enrique to replace Pedro and Neymar with youngsters Sandro and Munir El Haddadi in search of a breakthrough.
However, it was Malaga who enjoyed their best spell shortly after those changes as Roberto Rosales fired wide when well-placed at the edge of the box before Bravo produced a stunning save to turn Liverpool loanee Alberto's free-kick onto the post.