In Turin, Zlatan Ibrahimovic opened the scoring for Juve in the first minute with a cool finish before Mauro Camoranesi found the top corner of the net with a rising drive shortly after half-time. Davide Di Michele scored for Udinese in stoppage time.
Defeat left Udinese in fourth place, behind Inter Milan who beat Roma on Saturday.
Fiorentina improved their chances of avoiding the drop with a 2-1 home win over fellow strugglers Parma, while Brescia also gave themselves hope of retaining their top flight status by defeating Cagliari 2-0.
Sampdoria remain fifth despite losing 1-0 at Livorno where Cristiano Lucarelli grabbed the winner eight minutes from time.
Palermo are sixth after their 1-1 draw at Bologna, while Lecce thumped Chievo 3-0. Siena remain in danger of relegation after being held to a 2-2 draw by Messina.
Inter Milan, whose title challenge has been hampered by 15 draws, maintained their unbeaten record after beating Roma 2-0 at the San Siro.
Ronaldo's bash
Brazil striker Ronaldo gave his fiance a romantic Valentine's Day present on Monday, throwing a lavish engagement party at a sumptuous and secluded castle outside Paris.
Limousines drove guests into the grounds of the chateau amid tight security. Reporters saw Real Madrid midfielder Luis Figo and Italian designer Valentino arrive.
Brazilian media put the estimated cost of the party at around 700,000 euros (US$900,200), although they say the couple could earn 400,000 euros by selling exclusive photo rights to Spanish magazine Hola!.
The flower arrangements cost 70,000 euros and the hire of the castle 20,000 euros, according to Brazilian media. British DJ Fat Boy Slim was expected to perform during the party.
Ronaldo was top scorer at the 2002 World Cup and is a former World Player of the Year.
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