With Barcelona dropping points this week, but fourth-placed Sevilla winning, Atleti responded with a performance worthy of champions at Wanda Metropolitano, though it came with a nervy finish.
But Atleti failed to take the chances to make the scoreline more comfortable and, after Jan Oblak and the upright came to their rescue, La Real set up a grandstand finish through Igor Zubeldia.
Luis Suarez curled just wide and Marcos Llorente was denied by Alex Remiro as Atleti started as they meant to go on, with the pressure telling in the 16th minute.
Llorente was the provider with a weighted cross to the back post where Carrasco, having beat La Real's offside trap, controlled it and prodded a finish through Remiro's legs.
It was 2-0 12 minutes later when Suarez played in Correa, who coolly found the bottom-left corner.
With little to lose, La Real hit back, forcing Oblak into two brilliant saves, the second a fingertip onto the post to deny Alexander Isak.
Wasteful finishing plagued Atleti's second-half display, with Carrasco and Suarez fortunate not to be made to pay for poor misses when Portu crashed an effort against the post, with Stefan Savic making a heroic block.
Atleti were denied a fifth clean sheet in the space of six games when Zubeldia bundled in from a corner with seven minutes remaining, yet Simeone's men had the grit to hold on and put the title within reach.