In the second minute at the Nou Camp, the ball clearly ran out of play before Lucas Digne crossed for Deulofeu, who flicked it in off a superb backheel, leaving Malaga irate.
Barcelona struggled to break the visitors down as they searched for a second, which came in the 56th minute when captain Andres Iniesta fired home with the help of a deflection.
Luis Suarez missed a golden opportunity when set up by Sergi Roberto as the Catalans failed to score a third but still moved four points clear of second-placed Valencia, who beat Sevilla 4-0.
In the wake of protests in the city following the Spanish government's move to reduce the autonomy of Catalonia, the atmosphere was charged.
Fans chanted loudly for independence as usual, with banners demanding liberty and pro-independence flags being waved.
However things were much quieter on the pitch after Deulofeu's opener, with Barcelona struggling to break down Malaga's defence and even Lionel Messi finding it tough to make an impact.
The Argentine struck a free kick into the wall, while at the other end Malaga came close with Juankar's vicious cross headed wide by Chory Castro.
Messi came closer in the second half when he burst into life, forcing an impressive save from Andres Prieto after a classic dribble into the area.
It was a similar move that saw Barcelona eventually extend their lead, when Messi fed Iniesta, who saw his fierce shot deflected in.
LEADING PACK
Suarez should have added the third when Sergi Roberto played him in but somehow fired wide with the goal gaping, continuing a personal run of poor form with only three goals to his name this season in all competitions.
Barcelona, however, are in excellent shape and this was their eighth victory in nine league games, keeping them four points clear of Valencia.
Marcelino Garcia Toral's side continued their superb start to the season with a convincing victory over Sevilla at a vibrant Mestalla.
Goncalo Guedes followed up his brilliant strike against Real Betis last weekend with another stunning goal, beating two men and then rocketing a shot past the helpless Sergio Rico in the 43rd minute.
Simone Zaza doubled unbeaten Valencia's lead six minutes after the restart, notching his eighth goal of the season.
Santi Mina tucked home the third late on after being played in by the electric Guedes, with the 20-year-old Portuguese winger grabbing his second in stoppage time.
(Reporting by Rik Sharma; Editing by Christian Radnedge)
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