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Lionel Messi opened the scoring just three minutes into the match, heading in from a Neymar cross in the home side's first attacking move of the tie.
Neymar doubled their advantage shortly after in his first match since sustaining a fractured vertabra at the World Cup, chipping the ball over the keeper.
The visitors had a chance midway through the first half when Jose Juan Vazquez tried a long-range effort, but saw his strike parried onto the bar.
Barcelona continued to push as half time approached, resulting in a second for the Brazilian just before the break as he backheeled the ball in.
El Haddadi came off the bench for the second half and was on the scoresheet within 10 minutes, tapping in from close range from a Dani Alves pass.
Luis Suarez was introduced for the final quarter of an hour to make his debut for the La Liga club, but it was El Haddadi who extended their lead further, slotting the ball in from a Sandro Ramirez delivery.
Ramirez managed to add a goal himself in the final minutes of the match, rounding a couple of defenders before calmly firing the ball home.