Having won just one of their last eight games in all competitions, Atleti travelled to the Estadio Riazor in desperate need of a victory to resurrect their flailing campaign.
Thomas Partey scored a superb late goal as Atletico Madrid snatched a dramatic 1-0 win at Deportivo La Coruna to ease the pressure on Diego Simeone.
But a dogged defensive display from Deportivo exposed Atleti's early-season shortcomings once more.
That was, however, until Ghana international Partey produced a moment of sheer brilliance to snatch victory when the spoils looked certain to be shared.
The midfielder left it late but when he had the chance to make his mark he made no mistake, lashing the ball beyond Costel Pantilimon after a free-kick was rolled into his path.