Correa joined Inter from Lazio on Thursday and came off the bench to take the points for Simone Inzaghi’s side, who started their title defense with two wins from as many games.
The Argentine striker scored Inter’s second goal seven minutes from time, shot high to Matteo Darmian’s cross and made a comeback in the second half after Lautaro Martinez equalized with his own header shortly after the break.
The icing on the cake was added in stoppage time as he collected the ball and shot the third home with an accurate finish.
“I dreamed of coming here as a child. It was my first time wearing the Inter shirt and luckily we won thanks to my goals,” a cheerful Correa told Sky Sport Italia.
“I would like to thank my team-mates, my coach and the club for showing their trust in me and making me feel like I’ve been here for years.”
The defeat was tough for Verona, who deservedly took the lead in the 15th minute through Ivan Ilic and gave Inter a fight throughout the game, but they are pointless after the two opening games.
Inzaghi, who replaced title-winning coach Antonio Conte this summer, lets his new team sing from his anthem sheet.
After Edin Dzeko and Hakan Calhanoglu shone against Genoa last week, it was Correa’s turn to hit the headlines with his brace.
Martinez had a chance to give Inter the lead in the 13th minute of his season debut but his close-range snapshot was well saved by Lorenzo Montipo.
Verona took the lead just two minutes later through Ilic, who quickly read that goalkeeper Samir Handanovic would fit Marcelo Brozovic and pushed the ball away from the Croatian midfielder before scooping a stylish finish.
Inter dominated possession but looked unimaginative as the well-rehearsed hosts Dzeko and playmaker Calhanoglu initially kept the ball in check.
But Inter equaled right after the break, Dzeko pressed after a long throw from Ivan Perisic, which led to the ball falling off friendly for Martinez, who nodded into the house from close range.
After his 50th Inter goal, Martinez somehow missed seven minutes later after another long throw and a Dzeko snapshot. The Argentine’s left foot missed the target from a few meters.
Inter began slowly to squeeze Verona into their own half, but after a well-secured drive from Alessandro Bastoni Verona kept restricting their opponents to very little.
However, Correa saved with his Cristiano Ronaldo-esque header on the day the Portuguese superstar left Italy for Manchester United and his great second goal to keep the vibe in Milan going.
“I’m happy for ‘Tucu’,” Inzaghi, who headed Correa at Lazio, told DAZN.
“I’m glad he can enjoy this debut double because he’s a great player who will help us get results.”
In Friday’s early game, Udinese continued their encouraging start with a comfortable 3-0 win over Venezia following their opening weekend draw with Juventus.
Goals from Ignacio Pussetto, Gerard Deulofeu and Nahuel Molina gave Udinese from the far northeast around 100 kilometers from Venice after a dominant performance against the newly promoted team earned three points.