The winger took a touch to turn inside and beat his marker before firing low into the far corner of the net for a well-deserved opener.
Atleti then had a penalty call turned down on 41 minutes after Antoine Griezmann went to ground under a challenge by goalkeeper Oier Olazabal, with the France forward instead being shown a yellow card for simulation.
Griezmann made amends early in the second half by grabbing Atleti's second goal, rifling a half-volley in at the near post from the penalty spot after Sime Vrsaljko whipped a first-time cross towards his unmarked teammate.
Fernando Torres came on for Griezmann in the 58th minute and went on to get on the scoresheet midway through the half, expertly volleying into the left corner and well beyond the reach of Olazabal from Correa's delivery.
Levante could not muster up a response, their tentative forays being repeatedly repelled by La Liga's most miserly defence, and the final whistle would confirm a straightforward three points for Diego Simeone's charges.
ATLETICO MADRID (4-4-2): Oblak; Vrsaljko, Godin, Savic, Hernandez; Correa, Koke (Gabi 62'), Niguez, Vitolo (Juanfran 78'); Griezmann (Torres 58'), Gameiro
LEVANTE (4-4-2): Olazabal; Lopez, Cabaco, Pier, Abeid (Chema 78'); Jason (Bardhi 46'), Lerma, Campana, Morales; Marti, Sadiku (Lopez 46')