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It was the visitors who started strong and nearly took the lead in the 13th minute when the ball fell kindly for Neymar inside the area.
However, Gorka Iraizoz was equal to the Brazilian's effort, pushing it over the bar.
As the half wore on, Los Leones began to assert themselves, with Markel Susaeta in particular causing the Blaugrana problems.
Barca started the second period as they had the first, with Cesc Fabregas supplying Neymar to fire waywardly off target.
The game hinged on a contentious decision from the referee, who deemed Ander Iturraspe's foul on Neymar worthy of a yellow card, despite him being the last man and the Brazilian bearing down on goal.
When the breakthrough finally came in the 70th minute, it was a result of dogged work from Ander Herrera and a good cross from Susaeta, which was met by the arriving Muniain.
Toquero nearly made it 2-0 in the 77th minute, only to be denied by a fantastic reflex stop by Jose Manuel Pinto.
There was to be no rescue act, though, as Bilbao made it three wins in a row.