Goals from Gerard Pique, Messi and Adriano Correiaput Barca 3-0 up at the break, with Messi’s second-half strike putting him on 84 goals in all competitions for 2012.
Former Germany star Mueller holds the record for his 85 in 1972, and while Messi is near certain to break it before the Christmas break, his first goal may be given as an own-goal, although it was his at the time of writing.
Fabregas had added a thunderous fourth, his fifth Liga goal of the season, and while Athletic improved in the second half they only had one goal to show for it, Ibai Gomez finishing an Ander Iturraspelong ball that caught the defence ball-watching.
The result ensures Barca stay top of La Liga this weekend, while Bilbao – who now have the worst defensive record in La Liga – stay 14th but could slide as low as 16th by Sunday night.
With Athletic Bilbao missing the fatigued Iker Munian and continuing to leave contract rebel Fernando Llorente on the bench, their game was all about defensive resistance.
Initially they shaped up well, shutting out Messi and defending in numbers as Barca looked a touch frustrated.
But for all the good defensive work the visitors came unstuck at a set piece, leaving Pique unmarked to fire home from close range after Gorka Iraizozsaved Cesc Fabregas’s shot when Los Leones failed to clear a corner.
Messi added a second soon afterwards, although his clipped finish may have been going just wide as Fernando Amorebietaslid in on the line – replays were inconclusive as to whether it was the Argentine’s 83rd goal of the year, or an own-goal for the Venezuela defender.
Chasing the game, the visiting defence opened up as attempts to double-up on Messi saw others find space, Cesc Fabregas forcing a save from Iraizoz, Andres Iniesta putting wide of an empty net from a tight angle, and Messi himself hitting the bar after lovely wingplay from Iniesta and Jordi Alba.
Seconds after that chance Barca did have their third as Adriano fired into the roof of the net after a sweeping move initiated by Messi, Fabregas with a delightful through-ball to the Brazilian full-back.
The Basques at least brought Llorente on for the second half but, while he did give them more cohesion going forward, Barca were still very much in charge as Iraizoz denied Messi, who could have won a penalty after a clumsy challenge from Ander Herrara.
They got their fourth soon afterwards though and it was the best goal of the night – typical of Barca it was initiated by a thunderous tackle by Sergio Busquets, Iniesta then giving the defence the eyes as he fed Fabregas, who smashed a ferocious shot past the helpless keeper.
But Athletic had improved after half-time – Llorente and Ander both going close – and they pulled a deserved goal back when Gomez raced on to Iturraspe’s long pass before sliding it past the onrushing Victor Valdes.
Any faint hopes of a comeback were quickly put to bed though as Messi got his second of the night with a curling finish into the top right after an incessant spell of Barca pressure that saw defenders and keeper alike making desperate blocks.
It was a convincing win and one that ensures Barca stay clear of Atletico Madrid in second and – crucially – well ahead of the defending champions Real.