Barca have now put together 13 wins and a draw from their first 14 matches to beat the previous best start set by Real in the 1991-92 season.
Gerard Pique put the Catalan side ahead after 22 minutes followed quickly by Messi’s first, which came off defender Fernando Amorebieta on the line, before Adriano Correia hit the third on the point of half-time.
Cesc Fabregas then added to the deluge of goals and Ibai Gomez got a consolation before Messi struck again. Messi is now just one goal off Mueller’s record of 85 goals in a calendar year set for Bayern Munich and Germany in 1972.
Barca had their first sight of goal with a low drive from Andres Iniesta after 12 minutes which keeper Gorka Iraizoz saved comfortably.
Athletic failed to clear their lines from a corner and although Iraizoz repelled Fabregas’ shot, Pique pounced on the rebound to score. Minutes later and Barca doubled their lead. Athletic defender Amorebieta failed to keep tight to Messi, who slipped the ball past the ’keeper and a despairing dive from the defender.
Messi hit 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. Barca were guilty of easing off as Gomez pulled a goal back but Messi had the final say with his second.