Rayo were looking for a first win of the season and they took an unexpected lead in the 12th minute on Monday (Tuesday AEST) when Sergio Camello hammered home a cutback from Alvaro Garcia on the left.
Barcelona, however, bounced back almost immediately and were 2-1 up before the first period was even halfway over.
Raphinha equalised with a well-taken goal in the 18th and Lamine Yamal put them ahead 90 seconds later with a characteristic move, cutting in from the right and unleashing a powerful left-foot shot into the roof of the net.
Hansi Flick's men got a third after halftime when Florian Lejeune turned Gordon's cutback into his own net. Although the excellent Camello cut the deficit with a solid header, Raphinha soon made it 4-2 and Yamal rounded off the scoring with a low shot from just outside the box a minute from time.
The win moved Barcelona up to nine points from three matches and above Real Madrid at the top of the league on goal difference. Rayo sit third from bottom on one point - along with Celta Vigo, Valencia, Elche and Malaga.
"The first half we played very well. The reaction after the goal has been very good," Barcelona coach Hansi Flick said after the game.
"When we're winning 3-1 we have to control the ball better because we have the quality to do it. It's good to score, but ... we have to make the ball run.
"We have many matches left and even if we win 3-1, we have to learn to control the game. It's good that they want to score, but we have to control the game."
Elsewhere, Osasuna beat Getafe 1-0 to continue their unbeaten start to the season. The side from Pamplona are fifth after two wins and a draw. Atletico Madrid and Alaves are also on seven points.
