A fast start for the visitors saw Lamine Yamal miss a one-on-one in only the second minute, before Raphinha tried to chip on-loan Barça goalkeeper Inaki Pena from his own half in the fourth.
Keeping the pressure on, a simple ball from Dani Olmo found Yamal in the sixth minute, and he made no mistake for the opener.
Elche were unable to cope with the incessant pressure, as Ferran Torres and Olmo also went close soon after, and the only surprise was that there were no further goals as the clock hit the 20-minute mark.
Belatedly, Elche managed to get their first shot away, as Alvaro Rodríguez took aim in the 25th minute, but he fired wide.
Olmo then fired one against the crossbar after a mesmeric run from Raphinha, before Alvaro immediately beat Barça’s offside trap and drilled home the equaliser.
Barcelona continued to cause the Elche defence trouble, as Ferran hit the woodwork twice in the same move, but soon fired into the roof of the net from Frenkie de Jong’s assist.
With the away side firmly on top, Fermin Lopez missed two identical chances in two minutes before Ferran had another shot cleared off the line in the final action of what was an incredibly one-sided first half.
Alvaro bent a shot just wide with the first chance after half-time, before Rodrigo Mendoza’s effort was ruled out for offside, as the hosts came out strongly.
Barça again had the lion’s share of possession, with a number of half-chances going begging, before Adam El Mokhtari fluffed his lines when well placed at the other end.
Marcus Rashford then had a run on goal before putting another chance wide, but thanks to Yamal’s industry, belatedly powered home the visitors’ third with 20 minutes to play, marking the 10th goal of his Barça career.
That goal was enough to see out a result that means that Barcelona continue their sensational record of not having lost in the last 25 H2Hs (W21 D4), and will remain top of the table after the current round of fixtures, whilst Elche stay 12th ahead of Sunday’s games, having lost the second of their last 16 home league games (W7, D7).
Flashscore Man of the Match: Frenkie de Jong (Barcelona)