Filippo Inzaghi's side were forced to withstand considerable pressure for long periods of Sunday's game, with Napoli looking threatening going forward, but goals from Jeremy Menez and Giacomo Bonaventura proved decisive.
The contest was just six minutes in when French forward Menez strode into the Napoli area and coolly slotted into the bottom-right corner, giving Milan an early advantage.
Rafael Benitez's Napoli steadily improved, however, and forced Milan goalkeeper Diego Lopez into a number of crucial stops, most notably from compatriots David Lopez and Jose Callejon.
After just six minutes, Menez – starting in the central role – took Bonaventura's pass in his stride before bursting past Kalidou Koulibaly and stroking beyond Rafael for the opener.
Napoli did eventually grow into the contest, though, and Diego Lopez was forced into two saves in quick succession in the 22nd minute, first parrying away David Lopez's fierce effort before blocking Callejon's follow-up attempt.
The visitors piled the pressure on again just a few moments later, Callejon drawing a third save from his former Real Madrid team-mate after finding space in the right side of the area.
Andrea Poli almost doubled Milan's lead with a curling effort in the 34th minute, but Napoli continued to dictate proceedings.
And Benitez's men went agonisingly close to restoring parity three minutes before the break, as Milan defender Philippe Mexes poked Gonzalo Higuain's low cross just wide of his own goal.
With the hosts two goals up, Napoli started to look extremely susceptible on the counterattack and almost found themselves 3-0 down in the 60th minute, but Riccardo Montolivo steered wide after Keisuke Honda led a breakaway.
Napoli threw men forward in the latter stages and saw two presentable chances spurned by Higuain, but Milan kept Benitez's men at bay to secure victory and move to within two points of the UEFA Champions League places.
