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.
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.
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.
"NEW STRENGTH"
"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.
"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.
