Gennaro Gattuso's side had won three Serie A games on the bounce and secured a draw against Real Betis in the Europa League but a 2-0 loss to Juventus before the international break saw them head for the Italian capital searching for a positive result to put them back on track.
After battling with Simeone Inzaghi's men for 78 minutes, Kessie strike, with a bit of luck, from Davide Calabria's drag back looked to have secured the maximum points for the visitors but Joaquin Correa's smart finish from the edge of a crowded Milan box, deep into stoppage time, earned the hosts a share of the spoils.
The 21-year-old's third Serie A goal of the season on his 13th appearance was not enough for his team who would have swapped positions with the hosts had they won.
The San Siro outfit are still placed fifth with 22 points after 13 games while their hosts remain fourth, a point better their oppositions.
Kessie and Milan