Despite the effort of the 22-year-old Ivorian, the Red and Blacks failed to secure a Uefa Champions League ticket.
Hakan Calhanoglu put Gennaro Gattuso’s men in front in the 18th minute after he was set up by Kessie.
The Ivorian midfielder doubled the lead five minutes later after benefitting from Ricardo Rodriguez’s assist.
In the 28th minute, Francesco Vicari reduced the deficit for Leonardo Semplici’s men before Mohamed Fares brought his side level.
In the 66th minute, Kessie grabbed the match-winner with his second goal in the game from the penalty spot, but the Red and Blacks had to settle for a Europa League berth after finishing fifth on the table with 68 points from 38 games.
Kessie ended the season with eight goals from 42 appearances across all competitions.