An Alexis Sanchez brace helped Barcelona to a 4-0 victory over Rayo Vallecano on Tuesday which reduced Real Madrid’s lead to three points and showed they will not give up their title without a fight. Barca were given a quick chance to respond to their 1-0 away defeat to Getafe at the weekend as this fixture was brought forward due to the Catalan side’s involvement in the Club World Cup next month in Japan, and they ran out resounding victors. While Real have been in ominous form and recorded their 13th consecutive victory by beating local rivals Atletico Madrid at the weekend, Barca have stuttered recently away. At home though they have been as impressive as ever and with their victory over Rayo they have now scored 34 goals without reply at the Camp Nou. Barca coach Pep Guardiola was keener to praise Sanchez's impact on his return. "Alexis (Sanchez) isn’t a striker but he also can do this job which helps us a lot," said Guardiola. "He was injured for a while but before that he was very useful for us and then coming back he needed a bit of time. I have to congratulate him for his performance here." Rayo coach Jose Ramon Sandoval was satisfied that his team gave their best. "There was nothing for us to do but show our credentials by going out to win. We have given the Primera Division our style of football and I am more proud than ever of my players," he said. Barcelona started nervously until Sanchez gave them the lead after 28 minutes and then before the break the Chilean again and David Villa gave them a commanding advantage. Lionel Messi made it 4-0 four minutes into the second half. Andres Iniesta returned to Barca’s starting line-up while Cesc Fabregas, also fit again, was on the bench along with the rested Sergio Busquets. Promoted Rayo lost at home to Valencia on Saturday but they have had a fairly good start to their first top-flight campaign since 2002-03. The visitors from Madrid held their own in the opening stages and were unlucky not to take the lead with Lass Bangoura shooting wide from close range in only the third minute. Barcelona were tentative and struggling to find their rhythm, and while Dani Alves had a shot well saved by keeper David Cobeno, at the other end keeper Victor Valdes tipped a free-kick, which had been crossed in by Michel Sanchez, onto the crossbar. A goal for the home side did not look on the cards but then a moment of magic from Sanchez put them in the driving seat. He moved the ball from his left to his right foot and curled a shot in off the post from the edge of the area. It opened the floodgates as Rayo began to pay for their expansive play. Alexis prodded in a second after 40 minutes in slightly fortuitous circumstances with the ball coming back to him off Xavi Hernandez’s heel and then two minutes later Villa slotted into an empty net after being supplied selflessly by Dani Alves. After the break Messi burst away from Javi Fuego on the right wing before running in unchallenged on goal and finishing clinically to complete the scoring.