Simeon Verdi gave the hosts an early lead before Mbaye doubled their advantage - with his first goal of the season - in the 23rd minute.
Bologna ended the first half a man less after Vasilios Torosidis was sent off.
But that did not halt the Blue and Reds’ juggernaut as Okwonkwo, on the scoresheet earlier in the week and on as a 63rd-minute substitute for Verdi, was on hand to wrap the victory for Roberto Donadoni’s men in the 73rd minute.
The goal was the 19-year-old's third in six Serie A games this season.
Ghana midfielder Godfrey Donsah alongside M'baye were on parade for the entire duration of the tie.
The Senegal international opened his goal account after eight games, while Donsah has played 12 times and has two goals to his credit.
Bologna are currently seventh in the log after garnering 20 points from 14 Italian top-flight encounters.