Second-placed Valencia had closed the gap to one point after thumping Sevilla, but Barcelona, who are now eight points clear of third-placed Real Madrid, recorded their eighth league win of the season to move clear at the summit.
Barcelona boss Ernesto Valverde made two changes from the team that started against Olympiacos in the Champions League, with Gerard Pique and Paulinho dropping out for Javier Mascherano and Ivan Rakitic. Gerard Deulofeu kept his spot alongside Lionel Messi and Luis Suarez in the final third, but Jordi Alba was still injured.
As for Malaga, Diego Gonzalez and Zdravko Kuzmanovic both missed out through injury, while club captain Recio was suspended after his red card against Leganes last weekend. Keko came into the team in a wide position, and Diego Rolan again supported on-loan Watford Adalberto Penaranda in the final third of the field.
It took Barcelona just two minutes to make the breakthrough on the night as Deulofeu turned a Lucas Digne cross home from close range. It was an extremely controversial goal, however, as the ball was clearly out of play when Digne delivered back into the Malaga penalty box.
The hosts had a half-chance to double their lead in the 10th minute when Andres Iniesta delivered a dangerous cross towards Rakitic, but Malaga goalkeeper Andres Prieto, who was making his La Liga debut, just about did enough to unnerve the Croatian.
Penaranda had a long-range strike deflected wide of the Barcelona post in the 18th minute as Malaga committed players forward, before Chory Castro headed a Juan Carlos cross wide of the home side's goal on the 30-minute mark.
Messi was the player carrying the fight to Malaga as Barcelona looked for a second late in the first period, but the visitors were also still causing problems, and Castro should have done better after meeting a super Roberto Rosales cross in the final minutes before the half-time break.
The hosts had 80% of the ball in the first half, but only the one shot on target. Valverde resisted the temptation to make changes at the break, but Malaga were forced into an alteration as Juanpi replaced the injured Rolan, who tweaked his hamstring in the latter stages of the first period.
It was Malaga that had the first shot of the second half in the 51st minute, but Rosales's effort was always straight at Barcelona goalkeeper Marc-Andre ter Stegen, before Prieto kept out a low Messi strike down the other end.
Barcelona did have their second in the 56th minute, however, when Iniesta's strike, which was deflected off the foot of Malaga captain Rosales, found a route into the back of the net.
Luis Suarez just missed the post with a low strike five minutes later as Barcelona looked for a third, before Keko had a decent opportunity down the other end, with the attacker's goal-bound effort blocked by Digne.
Suarez had a glorious opportunity to make it 3-0 in the 74th minute after Roberto put one on a plate for the striker, but he somehow missed the target at the far post, and was replaced by Paco Alcacer for the final seven minutes.
Malaga were still active in the final third as Juanpi tested Ter Stegen late on, but Michel's team suffered their eighth league defeat of the campaign as they stayed bottom of the table on one point.