Bilbao finished the game with 10 men when Aymeric Laporte was sent off late on.
Iker Muniain put the Basques ahead with just five minutes played but Diego Costa pulled Diego Simeone's side level midway through the first half, and Koke dived in to head in the winner in the second half, allowing Atletico to preserve their one-point lead over Barcelona at the top of the table.
The result means that Atletico become just the second team to do the double on Athletic, as well as being responsible for two of the three times the Basques have lost at their new stadium San Mames Barria, adding to their 2-1 win in the Copa del Rey quarter finals in January.
But although it ended well for Los Rojiblancos, they were made to sweat for the three points, surviving two penalty scares in the second half, and once again were grateful to goalkeeper Thibaut Courtois for coming to their rescue.
Things began badly for Simeone's side, Mikel San Jose pumping the ball up field, Aritz Aduriz flicking it on and Muniain lifting it first time over Courtois, the ball landing just under the bar. Costa could have levelled on 13 minutes when played in by Koke, but hit his shot straight at Gorka Iraizoz.
But the forward, who scored the winning goal in January's meeting in Bilbao, was once again the thorn in Athletic's side, running onto an interception by Koke to face down Iraizoz again, this time shooting into the bottom corner.
Costa then dragged a shot wide of goal early in the second half, while Markel Susaeta squandered a chance to restore Athletic's lead towards the end of the first period, just heading wide of goal.
Costa was later denied a clear penalty when his leg was taken away by Laporte, but Atletico got their second goal a few moments later, Koke bravely diving in to meet a deflected cross from Filipe Luis.
Roared on by their famously passionate fans, Athletic went on the hunt for an equaliser.
Muniain fired wide of the near post and then Aduriz headed a Gaizka Toquero cross towards the top corner, but was denied by the outstretched hand of Courtois.
The hosts were furious they were not given one of two possible penalties, first when Aduriz was brought down by Miranda and then when Toquero fell after a challenge by Arda Turan.
Muniain shot just wide of the post from the edge of the box with eight minutes to go before Laporte was then sent off for a second yellow card as he brought Costa down when the striker was clean through, and Athletic were unable to create any more clear chances.