Diego Simeone's team saw an eight-match winning streak in the league come to an end when they were pegged back by Celta Vigo on Monday.
Real Madrid and Barcelona looked to be getting another favour when Granada substitute Yangel Herrera cancelled out Marcos Llorente's 63rd-minute opener on Saturday.
The unusually profligate Luis Suarez had gone close to breaking the deadlock numerous times, hitting the crossbar and finding Rui Silva in fine form, but a fifth successive away win seemed set to evade Atleti.
However, a huge slice of luck went Atleti's way when Correa's strike deflected in off Jesus Vallejo to settle the contest and move the visitors eight points clear.
Correa let Granada off the hook when he poked a one-v-one straight at Silva, before German Sanchez headed Granada's first opportunity wide.
Geoffrey Kondogbia's surging run resulted in an opening for Suarez three minutes later, but LaLiga's leading scorer could not generate enough curl to pick out the far corner.
Kondogbia and Suarez combined again 30 minutes in, yet Silva was equal to the latter's powerful effort, with Granada's goalkeeper denying Atleti's number nine again soon after.
Suarez went closer after the restart – a half-volley clipping away off the bar.
Another opportunity fell Suarez's way before the hour, but the former Barca star could not take the ball under control in the six-yard box.
Llorente finally found the opener when he drilled in from the edge of the box for his seventh league goal of 2020-21, but despite creating little of note, Granada snatched a swift equaliser three minutes later as Atleti failed to clear a corner and Herrera's effort deflected beyond Jan Oblak.
Yet Atleti had a deflection go in their favour 16 minutes from time, Silva helpless to prevent Correa's shot from looping in after Vallejo's attempted block.