Goals from Goran Pandev and Blerim Dzemaili earned Walter Mazzarri's side all three points at the Stadio San Paolo with Edinson Cavani seeing his penalty saved.
Napoli reduced the arrears on Juve, who beat Pescara 2-1 on Saturday, to nine points with seven games of the season left but, perhaps more importantly, they increased their advantage over the Rossoneri.
Massimiliano Allegri's Milan fell foul of a spirited recovery from 10-man Fiorentina, who earned a priceless point from a 2-2 draw in Tuscany.
Riccardo Montolivo put the visitors in front before Nenad Tomovic was given his marching orders. Things looked grim for La Viola when Mathieu Flamini doubled Milan's lead, but penalties from Adem Ljajic and David Pizarro salvaged a point for Vincenzo Montella's side, who remain six points behind their opponents.
Inter Milan are a further two points behind after a second-half hat-trick from German Denis saw 10-man Atalanta triumph 4-3 in a frenetic game at San Siro.
Veteran Tommaso Rocchi opened his account for the club in a tame first half before Ricky Alvarez cancelled out Giacomo Bonaventura's equaliser with a quickfire brace. But Denis promptly added two classy goals to a dubious penalty to fire Atalanta into 13th place and leave Inter's fans opened mouthed before La Dea's Cristian Raimondi saw red late on.
There was a new twist in the battle to avoid the drop as Siena and Palermo joined Genoa in a three-way tie for 17th place.
The Ligurians' defeat at Napoli saw them drop to second from bottom on goal difference with the Bianconeri and Rosanero matching them on 27 points thanks to mixed results.
Siena's point came from a goalless home draw with Parma, who remain 10th, while Palermo pulled off a surprise 3-1 win at Sampdoria. Steve Von Bergen scored first at the Marassi with Josip Ilicic and Santiago Garcia making Gianni Munari's effort for Samp an irrelevance.
Antonio Di Natale, meanwhile, returned to scoring form as his two goals guided Udinese to a 3-1 win over 16th-placed Chievo. Di Natale scored twice in five first-half minutes before Paul Papp pulled one back, only for Mehdi Benatia to seal victory at the death.
Udinese remain ninth, one point behind Catania, who were held to a goalless draw in Sicily by 11th-placed Cagliari.
Lazio take on Roma on Monday. The capital city rivals are sixth and seventh respectively with Lazio looking to pull six points clear in the race for Europe.