The Argentine forward, starting for only the second time in the top-flight this season, was at his explosive best to help Atletico recover from a chastening defeat by Club Brugge in the Champions League in midweek.
It has been a topsy-turvy start to the season for the 2014 and 2021 Spanish champions, who have struggled for consistency both in Europe and domestically.
Antoine Griezmann started the game, amid reports in Spain that Atletico and Barcelona have settled on a transfer fee to make his loan move permanent.
The French forward has mostly been used from the bench by Diego Simeone, as Atletico tried to avoid activating a pricy obligatory purchase clause in their initial deal.
Griezmann played a pivotal role in Atletico’s opener, with his clipped cross finished by Correa at the back post.
Former Southampton midfielder Oriol Romeu fired over at the other end after good work by Arnau Martinez, with Yangel Herrera heading another opportunity off-target.
Matheus Cunha should have doubled Atletico’s lead before half-time but was denied by Juan Carlos from close range. However, the goalkeeper was left with his tail between his legs three minutes into the second half, when Correa intercepted his pass with ease and stroked home.
Rodrigo Riquelme, on loan from Atletico, pulled Girona back into the game with a deflected drive from distance against his parent club.
Aleix Garcia forced a brilliant save from Jan Oblak with another long-range blast, and substitute Cristhian Stuani headed against the post from the resulting corner in a thrilling finale.
Later Saturday, Real Madrid, second, visit Getafe, and Athletic Bilbao welcome Jorge Sampaoli’s Sevilla.