Udinese's success kept the surprise package two points behind leading pair AC Milan and Juventus who both won away to stay top with 37 points from 17 games.
Zlatan Ibrahimovic converted a first-half penalty, controversially awarded for a foul by Thomas Manfredini on Alexandre Pato, and set up the second for Kevin-Prince Boateng in Milan's 2-0 win at Atalanta.
The Swede joined Di Natale and Atalanta forward German Denis, who hit the post from close range with the score at 1-0, as joint Serie A top-scorer with 12 goals.
Alessandro Matri's first-half goal gave unbeaten Juventus an unconvincing 1-0 win at bottom club Lecce where they were lucky to survive second half pressure in pouring rain.
Matri scored from close range when Massimiliano Benassi failed to hold Mirko Vucinic's low shot from 25 metres after Juve had lost midfielder Fabio Quagliarella to injury early in the game.
TOTTI PENTALTIES
Francesco Totti, 35, scored his first two goals of the season, both penalties, to give improving AS Roma a 2-0 win over Chievo.
The one-club Totti, who missed a penalty in the 1-1 draw with Juventus last month, opened his account in the 34th minute after a clumsy tackle by Nicolas Frey on Erik Lamela
His second, with 12 minutes left, followed a Bostjan Cesar handball as Roma moved up to joint sixth with 27 points alongside Napoli, who followed up their 6-1 win over Genoa before Christmas with a 3-1 win at Palermo.
Goran Pandev, Edinson Cavani and Marek Hamsik put Napoli 3-0 ahead before Fabrizio Miccoli's consolation for Palermo, where coach Bortolo Mutti's home debut ended with a deafening chorus of jeers from the few fans who stayed until the end.
Stevan Jovetic scored twice, the first a penalty, in Fiorentina's 3-0 win at Novara and Cagliari beat Genoa by the same score, handing Pasquale Marino an unhappy debut with the visitors after he replaced Alberto Malesani following a 6-1 defeat at Napoli.
Joaquin Larrivey converted an early penalty for Cagliari and Victor Ibarbo added the second just before the hour.
Genoa's misery continued with a straight red card for Emiliano Moretti before Andreas Granqvist put through his own goal.
In the early match, Udinese's Di Natale opened his account after only 48 seconds when he slid the ball home after Antonio Floro Flores sprang the offside trap and broke down the right.
Although Udinese were dominant, Brazilian forward Eder equalised for Cesena out of the blue in the 39th minute and it took a blunder from their goalkeeper Francesco Antonioli to put the hosts back in front.
The hapless Antonioli allowed Kwadwo Asamoah's low, swerving shot to slip under him in the 54th minute in what proved to be the game's turning point.
Cesena had Maurizio La
