Furious Siena, who went ahead in the 25th minute through Claudio Terzi, also had Christian Terlizzi harshly sent off in the 70th minute, almost immediately after Milan captain Massimo Ambrosini had been dismissed.
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Milan scraped into third place with 72 points, two ahead of Fiorentina who won 5-1 at Pescara with an Adem Ljajic hat-trick and are likely to feel hugely aggrieved by the manner of Milan's win.
Injury-ravaged Inter Milan's nightmare season ended with a crushing 5-2 home defeat by Udinese, who finished fifth and joined Fioretina in the Europa League next season. Inter finished ninth.
Serie A leading scorer Edinson Cavani scored Napoli's goal, taking his tally to 29, after Marquinho and Mattia Destro had scored for Roma.
Milan coach Massimiliano Allegri's future remained in the balance, despite receiving a late helping of good fortune in the historic Tuscan city.
"We finished the season the way we started, with suffering and difficulty," Allegri told RAI television.
Milan wasted a flurry of early chances as Antonio Nocerino fired wildly over from Ignazio Abete's cross and M'baye Niang missed the ball completely when all he had to do was turn in Robinho's cross from six metres.
But Siena showed they would not simply roll over and when Terzi was left unmarked, he headed in Alessandro Rossini's cross in the 25th minute.
Ljajic turned in Juan Cuadrado's low cross at the far post, then ran on to a Matias Fernandez pass to score, before Fernandez himself was on target with a low
