Milan's task was made more difficult after Sandro Tonali was sent off in the 33rd minute following a VAR review. The referee had initially shown the midfielder a yellow card for a dangerous tackle but changed it to red after consulting the pitch-side monitor.
Rafael Leao made it 2-0 four minutes into the second half, while the hosts missed a penalty.
Milan remain unbeaten and have 37 points from 15 games, one point ahead of Inter, while Benevento stay 10th.
"This was another tough victory considering the numerical inferiority," Milan manager Stefano Pioli told Sky Sport. "It was a great reaction and a great desire to bring home an excellent result.
"The group is young, they must continue to grow and improve. We are enjoying this victory."
Inter had laid down a marker in the title race with their hammering of Crotone and, with third-placed Roma also winning earlier on Sunday, the pressure was on Milan.
After Ante Rebic had won the spot kick, Kessie converted with aplomb, but Tonali's moment of madness saw him depart with just under an hour of the match still to play.
Robert Insigne hit the post for the home side and Gianluigi Donnarumma made some fine saves to keep Milan in front before Leao put them 2-0 up.
The hosts' chance to get back into the match came from the spot but Gianluca Caprari dragged his penalty wide, ensuring Milan, who hit the post twice chasing a third goal, could see out another victory in their quest for a first Scudetto in 10 years.