Three goals during a manic five-minute spell in the first half settled the match but did not typify an otherwise tepid encounter at the Wanda Metropolitano.
Atletico now have four consecutive victories across all competitions and moved back to within five points of city rivals Real Madrid, while the result ended a three-match winning streak for Levante.
The hosts almost scored in the first minute on Saturday when Correa's shot was saved, Joao Felix and Saul Niguez then unable to convert follow-up attempts.
But Atletico opened the scoring after 13 minutes when Thomas Partey found Kieran Trippier on the right and the defender's volleyed cross was converted by Correa's superb first-time finish.
Roger replied three minutes later when his volley deflected in off the arm of Alvaro Morata after he had latched on to Jose Campana's free-kick.
Atletico swiftly got back in front, though, Renan Lodi whipping in a left-wing delivery that Felipe impressively headed in from 12 yards out, his effort coming just 109 seconds after Roger's strike.
Correa's shot forced a good one-handed saved from Aitor Fernandez shortly before the break and the Levante goalkeeper also kept out an effort from Joao Felix just before the hour mark.
Joao Felix also fired wide from the edge of the area late on but Atletico were still able to hold on for victory in relative comfort, albeit Jan Oblak had to make two late saves to deny Enis Bardhi.
What does it mean? Atletico's poor run behind them
Atletico have won four straight games for the first time this season and have clearly overcome their dreadful run that saw them taste victory in just one of the previous eight.
Four straight wins and eight goals have Diego Simeone's men in better shape, but there remains plenty of work to do before the Madrid derby on February 1.
Felipe fabulous for Atletico
As well as scoring his first LaLiga goal, Felipe tested goalkeeper Fernandez with another aerial effort and recorded game-high totals for interceptions (4) and clearances (8).
Joao Felix frustrated once again
The Portuguese forward came into the match having played 572 minutes in LaLiga without scoring or providing an assist. Despite Simeone giving him 87 minutes, that dreadful run continued as he mustered only one shot on target and did not create a single opportunity for his team-mates.
Atletico will take momentum into their meeting with Barcelona in the Supercopa de Espana in Saudi Arabia on Thursday, while Levante do not play until a Copa del Rey tie with Real Jaen on January 12.