Sandro broke the offside trap to score against his former side and Jony grabbed a second with just minutes of the match remaining to deal a huge blow to the Catalan club’s title hopes.
Neymar compounded the misery for the visitors when he was sent off for a high challenge midway through the second half.
Barcelona are now three points behind leaders Real Madrid having played a game more than their rivals.
Back in November, the two sides played out a goalless draw at the Nou Camp, where Barcelona enjoyed 81 per cent possession and had 29 shots at goal and it with the way the game started, it looked like being a similar game in the south of Spain.
Luis Suarez was his typical busy self and when he was found with a fabulous over-the-top pass by Jordi Alba, the former Liverpool man controlled superbly on his chest, but found Carlos Kameni in his way.
But with Barcelona growing increasingly frustrated and looking uncharacteristically disjointed, Malaga would take full advantage and went ahead courtesy of a superb run-and-finish by former Barca striker Sandro.
Jeremey Mathieu – in for the injured Gerard Pique – looked to play the offside trap, but got his judgement horribly wrong, as Sandro timed his movement to perfection and sprinted beyond the defender to slot calmly beyond Marc Andre Ter-Stegen for his 11th of the season.
That goal would have been extra sweet for the Spain U-21 forward, who after spending three years with the Catalan club in both the B team and first, was sold in July last year.
Andres Iniesta was introduced at half-time to liven proceedings up in the middle of the park, but it was Malaga who looked the brighter and should have had a second when Sandro cut the ball across to Juanpi, but he could only fire straight at Ter Stegen.
Neymar – who had been poor for most of the game – summed up his performance with a needless high challenge on a Malaga defender and the referee quickly brandished a second yellow to give the Brazilian his marching orders, but not before he had a verbal spat with some fans en route to the tunnel.
That red card was the first in Barcelona colours for Neymar and the first the club had received since Javier Mascherano was sent off back in October 2015.
Barcelona, who had been so dominant in midweek when they beat Sevilla, looked bereft of ideas and even Lionel Messi found himself unable to influence the action like he so often does.
With time running out, Malaga broke down the other end and this time made it count, as Jony was on hand to calmly take the ball following a cut back and smash in the second to end Barca’s hopes of a comeback and stop them from scoring for only the second time this season.
