Diego Simeone's side qualified for the Champions League before the final matchday, but was fortunate to not fall behind in the first half at Reale Arena as Rafinha spurned multiple chances.
Atletico punished La Real for not making their dominance pay when De Paul thumped a wonderful strike home after 50 minutes, before Correa sealed victory.
The hosts pulled a goal back in the 93rd minute through substitute Jon Guridi, but it proved too late to mount a comeback; defeat leaving La Real sixth, having already sealed Europa League qualification.
Mikel Merino headed narrowly wide in the opening exchanges, before Rafinha inexplicably hit the post from point-blank range after Jan Oblak's parry from a low Alexander Sorloth drive.
Rafinha wasted another great opportunity as he curled wide when one-on-one with Oblak following Sortloth's offload, before the midfielder arrowed just off target on the stroke of half-time.
Alex Remiro thwarted a swerving De Paul effort from the edge of the area after the interval, while Matheus Cunha cannoned a deflected strike against the crossbar.
But De Paul broke the deadlock soon after when he drilled a fizzing right-footed attempt into the top-left corner.
Remiro rushed out to ensure Antoine Griezmann's goal drought continued, before Correa doubled Atletico's advantage with a curling finish in the 68th minute.
Guridi headed home from close range after Oblak parried Adnan Januzaj's free-kick, but Atleti held on for victory.