The hosts dominated proceedings at the Estadio Benito Villamarin but conceded against the run of play on the half-hour mark when a cross from the right was tapped home by Saul Niguez at the back post.
Atletico could have doubled their lead on 31 minutes when Correa found himself clean through on goal as Betis were caught out at the back, but his low shot was straight at the goalkeeper.
Despite enjoying 74% of possession, Betis could not make the most from their four shots on target, leaving Diego Simeone's side to leave Seville with all three points.
Real Betis (4-2-3-1): Adan; Barragan (Gacia 75'), Mandi, Feddal, Durmisi; Ruiz (Ruibal 88'), Guardado (Camarasa 66'); Joaquin, Boudebouz, Tello; Leon
Atletico Madrid (4-4-2): Oblak; Vrsaljko, Savic, Godin, Luis; Saul, Gabi, Partey (Hernandez 90+3'), Koke; Gameiro (Torres 76'), Correa (Gimenez 61')