From then on, Barca took control as Yamal latched on to an Alejandro Balde pass before cutting on to his left foot and firing brilliantly into the far corner for the ninth-minute opener.
The hosts doubled their lead two minutes later, Fermin Lopez pouncing on a slip from Adria Pedrosa before crossing for Torres to tap into an empty net.
Elche halved the deficit three minutes before the break through Mir who broke the offside trap before curling a shot brilliantly into the bottom corner from the edge of the box.
Rashford had the ball in the net early in the second half, but the linesman’s flag was up for an offside against Fermin in the build-up.
But the England forward wasn’t to be denied and found the net soon after, collecting a Fermin pass and powerfully firing beyond Inaki Pena from close range.
Mir hit the post twice in the second half, but wasn’t able to spark an unlikely comeback with his efforts.
Barcelona’s victory stretched their home record against Elche in La Liga to 25 matches without defeat, winning 18 of them.
