Ezequiel Lavezzi, who scored twice in Napoli's 3-1 Champions League last 16 first-leg win over Chelsea in midweek, was again on target as Inter suffered a seventh defeat in eight matches.
Inter boss Claudio Ranieri has been given the backing of president Massimo Moratti after dragging the 2010 European champions away from the drop zone since his appointment in September but seventh spot will not placate angry fans.
Fifth-placed Napoli had the better of the first half although Inter's Wesley Sneijder, whose return from injury has coincided with a shift in system and a flood of defeats, went close with a curling free-kick.
Argentine striker Lavezzi netted with a superb one-touch finish on 59 minutes after good running from Blerim Dzemaili and Napoli held on despite Salvatore Aronica being harshly dismissed for a foul and Inter's Giampaolo Pazzini flashing a header wide.
Udinese, in third, took advantage of leaders AC Milan drawing 1-1 with second-placed Juventus on Saturday by cutting the gap to the top to six points following a 3-1 win at Bologna.
Lazio, who went out of the Europa League on Thursday and almost lost coach Edy Reja, are on the same points as Udinese after ending a difficult week on a high thanks to Miroslav Klose's 12th league goal in a 1-0 win over Fiorentina.
Napoli's win meant they leap-frogged AS Roma, who had a day to forget as Atalanta's German Denis bagged a hat-trick in a 4-1 win for the mid-table hosts.
Roma's Francesco Totti was banned while fellow talisman Daniele De Rossi was left out for arriving late to a tactics session and watched from the stands as his side crumbled.
"De Rossi was late for a team meeting and we have clear rules. The coach did not want to pardon this tardiness, the rules must be respected," Roma sporting director Walter Sabatini told the club's TV channel.
Guido Marilungo was set up by Denis to grab a 10th-minute opener for Bergamo-based Atalanta, thriving back in Serie A despite a six-point deduction for match-fixing.
Another counter-attack led to Denis making it 2-0 and although new Italy call-up Fabio Borini hit back on 36 minutes, the second half belonged to Denis with Atalanta also helped by the dismissals of Roma's Pablo Osvaldo and Marco Cassetti.
Palermo were also reduced to 10 men but after just two minutes when Federico Balzaretti was sent off for a professional foul in a 4-1 defeat at Siena, who stay two clear of the drop zone after Lecce's 2-1 win at Cagliari.
Cesena remain rock bottom following a 1-0 reverse at Chievo and Novara are just a point better off having lost 3-1 at Catania.
