The Rossoneri, who had not won at the intimidating San Paolo for almost 13 years and were booed with almost their every touch, moved above Inter Milan and two points behind leaders Lazio after goals from Robinho and Zlatan Ibrahimovic.
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Sixth-placed Napoli had a host of chances and the excellent Ezequiel Lavezzi pulled one back with 12 minutes to go, somehow flicking the ball in off the bar despite being almost flat on the ground.
The ambitious home side, hoping to break into the top four this term, were ultimately undone by being reduced to 10 men just before half-time when Michele Pazienza handled the ball for a second time to pick up a second booking.
The midfielder turned around and marched off without any protest but Napoli coach Walter Mazzarri, whose designer suit was completely drenched by the downpour, shook his head in disbelief on the touchline.
Milan left back Luca Antonini had his head in his hands for different reasons after 10 minutes when he was involved in a sickening clash with Napoli's Christian Maggio and had to be carried off the field with a neck brace as a precaution.
ON-FIELD BRAWL
The visitors were already without injured defenders Thiago Silva, Gianluca Zambrotta, Marek Jankulovski and Ignazio Abate - as well as Ronaldinho - so 2006 World Cup winner Oddo was called off the bench despite hardly ever featuring these days.
The right-back made the most of his chance by performing a neat one-two with Ronaldinho's stand-in Robinho, who sidefooted the ball into the corner from just inside the area after 22 minutes.
Oddo's 73rd-minute cross was then headed in by an unmarked Ibrahimovic, who later limped off with a knock but still managed to get involved in an on-field brawl from the bench.
The off-colour Swede and strike partner Alexandre Pato had other efforts for Milan, chastened by a 2-0 defeat at Real Madrid last week but increasingly looking like major challengers for the scudetto for the first time since winning it in 2004.
"It was a difficult match, we defended well and it's a very important three points for us," Robinho told Sky TV.
"I'm used to playing further forward but it's fine behind the frontmen too," added Robinho who netted his second league goal of the season after being slow to settle since his August move from Manchester City.
Milan, bidding to stop Inter claiming a sixth straight league title, host old rivals Juventus on Saturday.
