Luis Suarez hit the crossbar early in the second half as Diego Simeone’s side looked for a breakthrough.
Marcos Llorente put them ahead with a low drive from 20 yards but Yangel Herrera levelled soon afterwards as Atletico failed to clear a corner.
Angel Correa scored the winner with a heavily deflected strike which looped over the goalkeeper.
Atletico are eight points above defending champions Real Madrid – with a game in hand on Zinedine Zidane’s side.
Barcelona, who host Alaves at 20:00 GMT on Saturday, are three points behind Real.