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.
But Milan ultimately made Napoli pay for their wastefulness in front of goal as Bonaventura, integral for the opening goal, guided a glancing header past Rafael at the start of the second period.
The visitors cranked up the pressure during the final 15 minutes, but were unable to make the most of their superiority and Milan held on to claim victory to draw level with Napoli on 24 points.
With flu keeping the under-fire Fernando Torres out, Inzaghi opted to start without a recognised centre-forward and that decision had the look of a masterstroke early on.
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.
Milan appeared to tighten up in midfield at the start of the second half and soon doubled their lead in the 52nd minute, Bonaventura nodding in a cross from former Napoli full-back Pablo Armero.
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.
Menez then went close again just a couple of minutes later, seeing his driven effort deflected over by Koulibaly after a darting run through the Napoli midfield.
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.
