Atletico Madrid remain level on points with the Catalans as they too were 3-0 winners over Valladolid on Saturday.
Adriano got Barcelona off to a flying start when he curled home the opener inside two minutes.
Lionel Messi doubled Barça’s lead before half-time with a delightful lob over Ruben Martinez.
The Argentinian then teed up Alexis Sanchez to make it three before Pedro rounded off a wonderful team move involving Andres Iniesta and Cesc Fabregas.
Messi got his second of the evening midway through the second-half to overtake Real Madrid legend Alfredo di Stefano as the third-highest scorer of all-time in La Liga on 228 goals.
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.
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 Barça laid seige upon the Rayo goal in the early stages.
However, Victor Valdes had to be alive to prevent the visitors levelling when he bravely parried the ball away from the feet of Alberto Bueno before blocking Iago Falque’s follow-up effort.
It seemed only a matter of time before Barca found a second goal, though, and it duly arrived when Messi clipped home Fabregas’ pass over the advancing Ruben.
The four-time FIFA Ballon d’Or winner turned provider seven minutes after half-time as his through ball was dispatched by Alexis Sanchez for his 15th league goal of the season.
Barça’s best was yet to come as a sensational backheel from Iniesta freed Fabregas inside the area and he unselfishly squared for Pedro to slot home from close range.
Neymar was then introduced for the first time in three weeks, but it was Messi who was next on the scoresheet as he slotted Sanchez’s pass into the far corner.
Messi was then withdrawn to keep him in reserve for the Etihad on Tuesday, but Barça’s hunger for goals continued and Neymar rounded off the scoring as he fired brilliantly into the top corner from outside the area.
Earlier, two goals inside the first four minutes guided Atletico to a comfortable win over Valladolid.
After three consecutive defeats in league and Cup it was imperative for Diego Simeone’s men to get back to winning ways if they were to maintain their title challenge and they couldn’t have made a better start.
Raul Garcia opened the scoring from a well-worked free-kick after three minutes before Diego Costa lofted in his 25th goal of the season 60 seconds later.
And Diego Godin rounded off the scoring when he headed home the third from Koke’s corner 17 minutes from time.
Elsewhere, Levante defeated Almeria from an impressive David Barral strike to move up to seventh in the Primera Division table, while Celta Vigo won at Villarreal thanks to goals from Fabian Orellana and Nolito.