Valencia remained just two points behind the Catalans at the top of the table with a 3-1 win over champions Atletico Madrid thanks to three goals in the opening 13 minutes.
After resisting some early pressure from Rayo, Barcelona killed the game off with two goals in as many minutes just after the half hour mark as Messi and Neymar took advantage of the hosts' high line to continue their fine goalscoring form.
Rayo were reduced to nine men after half-time as Jorge Morcillo and Javier Aquino were shown second yellow cards and Barca saw the game out to preserve their record of not conceding so far this season in La Liga.
"When you play on a pitch as small as here, playing with intensity is essential and I think we were up to the task," said Barca boss Luis Enrique.
Claudio Bravo now holds the record for an unbeaten start to a La Liga season and Barca's Chilean goalkeeper needed to be at his best early on to prevent Alberto Bueno firing Rayo into the lead.
Meanwhile, on Atletico’s defeat to Valencia, boss Diego Simeone said: "Valencia started very strongly and we made mistakes that we don't usually make.
"After that Atletico played very well and they didn't have any more chances. If we had scored the penalty, perhaps it would have been different."
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