Los Colchoneros' bid for a first top-flight title since the 2013-14 season had faltered in recent weeks, but just a second win in six games keeps them a step ahead of neighbors Real Madrid. This result meant Real stood four points behind Atletico heading into a clash with Getafe later on Sunday.
Despite a dismal start, which did not herald a shot until the 34th minute, Atleti went in at the break two goals to the good.
The man who made the breakthrough grabbed a second goal just two minutes later, superbly turning Anaitz Arbilla after collecting Carrasco's pass before slotting past Marko Dmitrovic from close range for his sixth goal of the season.
The hosts extended their advantage four minutes after the restart, Carrasco latching onto Saul Niguez's long ball over the top, rounding Dmitrovic and rolling into an empty net.
Correa turned provider for Atleti's fourth in the 53rd minute, his low pull-back into the middle of the penalty expertly dispatched by Llorente into Dmitrovic's bottom-right corner.
Llorente scored his 11th LaLiga goal of the season in the 68th minute, controlling Carrasco's pass before firing a half-volley past a hopelessly exposed Dmitrovic as Atleti sealed all three points in style.