Correa struck twice in a 5-0 thrashing of Eibar and he opened the scoring at the Wanda Metropolitano with a deflected strike.
Carrasco eased the nerves with a second goal - his third in as many matches - 10 minutes from time to put Atleti three points clear of Real Madrid with six games to go.
Diego Simeone's Atletico side ought to have won by a more emphatic margin a day after it confirmed its withdrawal from the collapsed European Super League.
Yet Dimitrios Siovas should have given Huesca a shock third-minute lead when he shot straight at Jan Oblak from close range after Atleti failed to deal with a free-kick from the left.
Alvaro Fernandez produced a sharp double save at the other end to deny Carrasco and Saul Niguez, and then Correa opened the scoring six minutes before the break.
The in-form forward turned sharply after taking a pass from Marcos Llorente and beat Pablo Insua before finding the back of the net with a deflected left-footed strike.
Atleti picked up where it left off after the interval, with Fernandez making himself big to keep out Koke's effort from close range.
The busy Huesca goalkeeper was called into action again to palm Renan Lodi's drive away for a corner as Simeone's men continued to dominate.
Sergio Gomez came agonisingly close to equalising when his free-kick flashed wide of the post before Fernandez beat away another effort from Niguez.
Carrasco gave Atleti breathing space, tapping in after Llorente unselfishly squared the ball as Huesca appealed for offside. The goal was awarded following a VAR check.
Dani Escriche should have pulled a goal back in the closing stages when he stabbed wide from point-blank range, as Huesca's survival hopes suffered a blow.