Correa missed Thursday’s win over Osasuna with a knee sprain he sustained in the Madrid derby triumph last weekend but said he came back as soon as possible to help Atletico.
“I wanted to force it, with a bit of pain, to help the team and it turned out well,” said Correa, who started in attack in place of the suspended Alvaro Morata.
“Today the coach told me that I should play as the number nine to give more freedom to (Antoine) Griezmann.”
Atletico were on top from the start, with Griezmann striking the post before Lucas Pires sent the visitors ahead at the Metropolitano.
The Brazilian winger finished off Chris Ramos’s excellent low cross to the far post, although Atletico were angry a foul was not given in the build-up.
Cadiz defender Fali came close to doubling his side’s lead with a cheeky lob from inside his own half, which flew over Jan Oblak but also narrowly wide, to the goalkeeper’s immense relief.
However Roger Marti produced a special chipped finish to beat Oblak and double Cadiz’s lead.
Correa headed home at the other end from Cesar Azpilicueta’s cross to start Atletico’s comeback after 32 minutes.
Molina then drilled home after a rebound fell into his path at the start of the second half to level the game.
“We wanted to hold on for those first minutes (of the second half), we knew they would throw everything at us, but it wasn’t to be,” said Cadiz forward Marti.
An Atletico winner seemed inevitable and eventually Argentina international Correa polished off a slick team move, turning home Saul Niguez’s cutback.
“(Saul’s form) is a prize for his humility, hard work, not giving up … for all the work he’s done in the last few years he deserves the moments he’s getting right now,” added Simeone.
Atletico have played one fewer game than the teams above them and are three points behind third-place Girona.
Leaders Real Madrid beat the Catalan minnows on Saturday and are five points clear of Atletico, with champions Barcelona second after their win over Sevilla on Friday.
Elsewhere Real Betis earned an impressive 3-0 win at home against Valencia to move seventh.
Youngster Assane Diao, 18, scored for the second match running in his second game in the Spanish top flight, with Marc Roca and Ez Abde rounding out the victory.
Five-minute hat-trick
Earlier bottom-of-the-table Almeria threw away a three-goal lead earned by a five-minute Luis Suarez hat-trick in an entertaining 3-3 draw with Granada.
The hosts, under interim coach Alberto Lasarte after Vicente Moreno was sacked in the week, took control thanks to the Colombian striker’s remarkable rapid-fire treble.
Suarez netted three goals all at the end of the first half, each set up by winger Largie Ramazani, in the space of five minutes and 24 seconds.
It was the third-fastest treble of the 21st century in La Liga — Kevin Gameiro holds the record after he scored a hat-trick for Atletico Madrid in four minutes 43 seconds against Sporting Gijon in 2017.
Later Suarez was taken off injured, with Spanish reports saying he has sustained a shin fracture which could keep him out for three months.
Granada hit back through Bryan Zaragoza with a penalty, after his team-mate Antonio Puertas missed a spot kick earlier in the second half.
Ricard Sanchez and Myrto Uzuni completed the comeback for Granada, 19th, two points above winless Almeria.
Excellent
Atletico beats Cadiz with strong comeback as Correa brace helps