Eder Martins gave the hosts a two-minute lead but former Nerazzuri forward Rodrigo Palacio drew Roberto Donadoni’s men levelled in the 24th minute.
After the restart, Yann Karamoh netted the decisive goal that gave Luciano Spalleti's men maximum points in the 63rd minute.
Moments later, Bologna were faced with an uphill task to salvage the situation as Mbaye was shown two yellow cards in the spate of four minutes while Adam Masina was shown a straight red card in the additonal time by referee Paolo Valeri.
68' The Rossoblu down to ten after Mbaye receives his second yellow card for a foul on Rafinha. #InterBFC 2-1— Bologna FC 1909 (@BolognaFC1909en) February 11, 2018
Bologna remain 13th in the Italian top-flight table with 27 points from 23 games and they will be chasing their first maximum points since their 3-0 win over Benevento on January 21, when they host Sassuolo at the Stadio Renato Dall'Ara on February 18.