Lazio also stayed one point behind Juve after a 3-0 win at Cagliari in the late match.
Cesena fired coach Marco Giampaolo after a 2-0 defeat at Parma left them winless and rooted to the bottom while Fiorentina coach Sinisa Mihajlovic was angry with fans who jeered his team in a 1-0 win over Genoa.
Two goals from Mattia Destro helped Siena to a 4-1 victory over Chievo while struggling duo Lecce and Novara drew 1-1.
German Denis scored his sixth goal of the season but the Argentine's seventh-minute effort was not enough for Atalanta as they slumped to a 3-1 defeat at Bologna.
Di Natale, who once again tops the scoring charts, took advantage of slack marking in the 38th minute to turn in Dusan Basta's cross as Udinese bounced back from Wednesday's 2-0 defeat at Napoli.
Udinese lost their unbeaten record in that match when the irrepressible Di Natale was missing through injury.
Lazio soaked up early pressure in Sardinia, then hit their hosts with two goals in a five-minute spell before half-time from Senad Lulic and Miroslav Klose. Tommaso Rocchi completed a somewhat flattering scoreline two minutes from time.
Sunday's results left Udinese and Lazio with 18 points from nine games, one behind leaders Juventus who beat Inter Milan 2-1 away on Saturday.
Defending champions AC Milan, 3-2 winners at AS Roma on Saturday, are fourth with 17 points.
Bottom club Cesena said on their website that Giampaolo, who took over in the close season, had been dismissed following the defeat at Parma and a new coach would be named in the coming days.
The Sea Horses have just three points from nine games after Gabriel Paletta and Alessandro Lucarelli scored in each half for Parma.
"It's a change that I had to make to give new strength and enthusiasm to the team," club president Igor Campedelli was quoted as saying by the ANSA news agency.
Lecce coach Eusebio Di Francesco also had to fend off talk about his future after the draw with Novara left his side two points above Cesena in 19th place.
"Nobody's said anything to me, when I talked to the directors it was about the game," he said.
"That question should be asked to the club."
Andrea Lazzari's goal gave Fiorentina a 1-0 win at home to Genoa but there was no fun in the result for Mihajlovic after fans jeered him and the team.
"It doesn't bother me but I'm unhappy for the boys," he told reporters.
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