Ivan Ilic intercepted a poor Samir Handanovic pass and chipped the keeper to give the hosts a shock lead.
Lautaro Martinez levelled with a header from a flicked-on long throw-in.
Correa, on loan from Lazio, headed Matteo Darmian’s cross into the top corner and then hammered in a second in injury time from 20 yards.
Inter only completed the signing of the 27-year-old Argentina international the day before the game.
Simone Inzaghi’s side beat Genoa 4-0 in their season-opener on Saturday.