Lionel Messi at double as Barcelona make record start
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Fernando Amorebieta failed to keep tight to Messi who through on goal slipped the ball past the keeper and a despairing dive from the defender only served to help the ball over the line.
The Barca players were queuing up to score the third before the break with Fabregas having a shot saved and Messi hitting the post before Adriano burst in from the right and fired a Fabregas pass into the roof of the net.
There was no let up after the restart and Iraizoz did well to block Messi but could do nothing to stop Fabregas who fired home an Iniesta pass inside the area.
Barca were guilty of easing off as Gomez pulled a goal back but Messi had the final say with his second.
Meanwhile, Mauricio Pellegrino was sacked as manager of Valencia following his side's 5-2 defeat at home to Real Sociedad.
The game swung on the first half dismissal of Jonas Goncalves with Valencia ahead through Roberto Soldado.
Alberto De la Bella equalised before the break and further goals came from Mikel Gonzalez, Diego Ifran, Imanol Agirretxe and Carlos Vela from the penalty spot while Soldado also got a second.
Earlier an Alberto Lopo header saw fourth-placed Malaga lose 1-0 away to Getafe.