Antonio Conte's side had home-ground advantage in Naples on Monday (Tuesday AEST) in a cagey encounter that looked to be heading for a stalemate until the 79th minute, when a swift attack down the left paid dividends.
Mathias Olivera's cross caused panic in the Milan defence and substitute Politano emerged at the far post to sweep home a crisp left-footed effort.
Victory took Napoli two points above the visitors but played into the hands of leaders Inter Milan, who now hold a seven-point advantage.
Juventus moved within a point of Como in the battle for a Champions League place.
While Cesc Fabregas's fourth-placed side were held to a goalless draw at Udinese, Juve banked a 2-0 win over Genoa to chip away at the gap.
Bremer and Weston McKennie scored the goals, both netting in the first 17 minutes, before Aaron Martin missed a second-half penalty.
Atalanta also kept their hopes of seeing European action next season afloat, with Giorgio Scalvini, Nikola Krstovic and Giacomo Raspadori scoring in a 3-0 win at Lecce.
In Spain's top-tier LaLiga, third-placed Villarreal were undone 1-0 in their visit to Girona.
The only goal came in first-half stoppage time when Pau Navarro sent the ball into his own net.
Villarreal remained in third spot, nine points behind Real Madrid and 18 adrift of leaders Barcelona.
Girona climbed two places into 12th place, one point behind Osasuna, Espanyol and Athletic Bilbao.
- with AP
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