Following Barcelona's loss to Valencia yesterday, Atleti just need a point against Sociedad to move into first place.
Soon after, the hosts did have the ball in the net, but David Villa's effort was ruled out for offside after he had rounded Bravo and rolled home.
It would be Villa who would break the deadlock in the 38th minute, sweeping home Costa's low cross from the left.
The Spaniard wasn't on the field for much longer, though, as he had to be withdrawn soon after the goal because of injury.
Follow the second half on Sports Mole here.