Messi’s opener had a touch of fortune as it came from a deflected free-kick and he set up Luis Suarez for the Uruguay forward to double the advantage before halftime.
Athletic refused to lie down and Mikel Rico pulled a goal back on the hour mark before Messi’s goalbound header was then turned into his own net by Oscar de Marcos.
The Catalan giants went 4-1 ahead when Neymar scored his 23rd of the season, Messi again with the assist.
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It took a late winner from Leandro Paredes to give Rudi Garcia’s men a first win after four league draws.
Napoli consolidated third place with a 3-1 home win over Udinese, while Samuel Eto’o made his debut for Sampdoria off the bench but his new team was held 1-1 by Sassuolo to stay fifth.
