Winger Deulofeu ended a 16-game wait to open his account in Barca colours by striking after only 113 seconds to conclude a move that had seen Lucas Digne carry the ball out of play before setting him up.
Andres Iniesta netted his first goal for club and country in over a year after the break to end any hopes of a Malaga comeback.
Barca were far from their free-flowing best against a Malaga side they failed to beat either home or away last season, the only LaLiga team they did not get the better of.
However, the victory saw Ernesto Valverde's men restore a four-point lead over closest challengers Valencia, who thumped Sevilla 4-0 earlier on Saturday, at the top of the table.
Rivals Real Madrid sit eight points adrift in third and are at home to Eibar in their game in hand on Sunday.
Malaga fumed at Barca's opener, which saw Digne's initial attempted cross deflect back to him off away captain Roberto Rosales before the France international clearly touched the ball beyond the byline and crossed for Deulofeu to flick in a clever volley from inside the six-yard box.
Lionel Messi wasted an excellent free-kick opportunity from 20 yards out, firing against the wall, while Gonzalo Castro headed wide from a good opening at the other end, having been set up by Juankar on the counter-attack.
There were few other clear opportunities at either end until Castro completely miskicked a volley from eight yards as Malaga, who lost Diego Rolan to a hamstring injury, went into the break one down.
Messi tested Andres Prieto for the first time early in the second half, forcing the away goalkeeper to get down sharply after creating a yard of space for himself.
Barca found their second goal in the 56th minute. Javier Mascherano and Messi were involved in the build-up before Iniesta took one touch and saw his left-footed shot deflect off Rosales and loop into the top-right corner from 12 yards.
Luis Suarez struck the side netting after producing a sharp turn and strike following Ivan Rakitic's pass, while Keko claimed for handball at the other end after his initial shot struck Digne and his follow up went straight to Barca keeper Marc-Andre ter Stegen.
Suarez then missed a glorious opportunity to net in back-to-back league games, failing to find the target after Sergi Roberto embarked on a rampaging run before laying the chance on a plate for his team-mate.
Malaga came close to getting one back when Luis Hernandez sent a good header wide, while Messi had the ball in the net just before full-time. However, an offside flag as the Argentina forward headed Samuel Umtiti's flick-on home meant he ended the match with just an assist to his name.
Barca continue to set the pace in the title race as Michel's side remain rooted to the bottom of the table with just one point from nine games.
