Atletico Madrid remain level on points with the Catalans as they too were 3-0 winners over Valladolid yesterday.
Adriano got Barcelona off to a flying start when he curled home the opener inside two minutes.
Lionel Messi doubled Barca's lead before half-time with a delightful lob over Ruben Martinez.
The Argentine then teed up Alexis Sanchez to make it three before Pedro rounded off a wonderful team move involving Andres Iniesta and Cesc Fabregas.
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And Neymar rounded off a perfect evening for the hosts on his return from a sprained ankle when he blasted home the sixth from long-range two minutes from time.
"Today was probably the best (game of the season) because we had intensity, we pressed well, our passing was good and we knew when and when not to play out from the back," said Barca boss Gerardo Martino.
"Results always change the opinion of the game, but for me the first half against Valencia or second-half against Sevilla were as good as today.
Martino had handed a rest to Xavi Hernandez, Javier Mascherano and Jordi Alba with the City clash in mind, whilst Neymar was named on the bench after a month out.
Adriano was one of those handed a start by the changes and he took just 90 seconds to make his mark with a fine strike from 25 yards.
Messi and Pedro were then unfortunate to both strike the woodwork as Barca laid seige upon the Rayo goal in the early stages.