The victory places Stefano Pioli's team back into a Champions League qualification spot, taking them provisionally to the third position with 44 points, along with Inter Milan.
Milan has won two consecutive league games for the first time since the World Cup break, putting them one step closer to their first Champions League quarterfinal in 11 years.
Monza challenged Milan early, but the visitors' defense remained intact, and goalkeeper Ciprian Tatarusanu made crucial saves to keep Milan's lead. Monza coach Raffaele Palladino was proud of his team's performance, although the loss ended their unbeaten run of eight games.
Theo Hernandez had a chance to double Milan's lead, but his shot went wide.