Iker Muniain steered home the only goal of the contest 20 minutes from time as Barca slipped to a second loss in five days following their disjointed defeat to Ajax in the Champions League on Tuesday.
While the loss in Europe can be absorbed, defeat in La Liga is much more damaging with Gerardo Martino's men now level with Atletico Madrid at the summit on 40 points, three clear of a Real Madrid side who appear to finally be hitting their straps.
Barca have struggled since losing Lionel Messi to a hamstring injury and knew they would be up against it at Athletic's new 53,000-seater stadium, where the hosts had looked mighty in winning five and drawing two of their first seven league games there this season.
Neither side came out of their shell in the opening half with Barca threatening just once, in the 11th minute, when the ball broke to Neymar inside the area but his curling shot was clawed away by the agile Gorka Iraizoz.
The best chance of the half went the way of the hosts in the 29th minute when Markel Susaeta's cross took a deflection and ran through to Muniain but the forward failed to make a telling connection and Jose Pinto gathered.
The hosts had a let-off on 57 minutes when Ander Iturraspe was shown only a yellow card when he hauled down Neymar on the edge of the area with the Brazilian through on goal and ready to pull the trigger.
Neymar, who had struggled with his footing to such an extent in the first half he was required to change his boots, took the resulting free-kick but saw his effort sail just wide.
Just after the hour Athletic were on the attack with Gaizka Toquero rising to meet Susaeta's centre but Pinto gathered his header comfortably.
Barca threatened moments later when Martin Montoya stole in behind the defence to latch on to Andres Iniesta's lofted through ball but Mikel Balenziaga tracked across well from left-back to smuggle the ball out for a corner.
The breakthrough came in the 70th minute when Athletic broke away down the right, the ball eventually coming to the ever-threatening Susaeta whose low ball into the area was tucked home first-time by the inrushing Muniain.
With Barca wobbling and on the brink of first back-to-back defeats since March, the hosts looked to press home their advantage and Toquero should have done better with a free header in the 74th minute that brought Pinto into the action once again.
Athletic remained on the front foot as Barca ran out of ideas and might have added a second when Aymeric Laporte rose highest at a corner but saw his header drop just over.