A 2-0 win for second-placed Napoli at bottom side Bari made the day worse for Inter, who have a game in hand in fifth but now trail leaders Milan by nine points and the Neapolitans by five just over halfway through the campaign.
On the plus side for Inter, title-chasing Lazio lost 3-1 at Bologna and injury-hit Juventus drew 0-0 at coach Luigi Del Neri's former club Sampdoria in a scrappy encounter with Alessandro Del Piero missing a great chance in stoppage time.
Inter's Dejan Stankovic slammed in a 16th-minute opener from Thiago Motta's pass but defender Cristian Zapata soon equalised for eighth-placed Udinese with a powerful left-foot shot which Luca Castellazzi failed to stop.
Serie A top scorer Antonio Di Natale curled a superb 25th-minute free kick into the bottom corner and Maurizio Domizzi exposed more questionable goalkeeping from stand-in Castellazzi in the second half.
The European champions had won five straight games in all competitions since Leonardo replaced Rafa Benitez on December 24, sparking hopes of an incredible scudetto-winning comeback, but the Brazilian was undone in a niggly game.
"We started well but then an Udinese in great form came to the party," former Milan boss Leonardo, who had Julio Cesar, Wesley Sneijder and Diego Milito out injured, told Sky.
"When they play like that, it's difficult for everyone."
TROUBLED FIORENTINA
Milan, beaten at Cesena at the start of the season and coming off two league draws, nervously beat the promoted side 2-0 on a relaid San Siro pitch thanks in part to Maximiliano Pellegrino's second own goal in two games just before half-time.
Antonio Cassano set up the chance with another great pass on his first Serie A start for Milan before Zlatan Ibrahimovic scored late on, but the hosts' lengthy injury list grew with defender Alessandro Nesta suffering a shoulder problem.
AS Roma went second on Saturday with a 3-0 win over Cagliari but Napoli leapfrogged Claudio Ranieri's team thanks to Ezequiel Lavezzi and Edinson Cavini scoring either side of the break at rock-bottom Bari who were reduced to 10 men.
Lazio, strugglers last term, made a flying start to the campaign but inconsistency has set in for Edy Reja's outfit.
The Romans, who omitted striker Mauro Zarate amid media speculation of a row with Reja and a bid from Juve, led through Sergio Floccari's early goal but Gaston Ramirez and Marco Di Vaio (2) hit back for Bologna who continue to make light of their ownership problems. A player brawl marred the end.
Troubled Fiorentina, who drew 1-1 with lowly Lecce, were missing the banished Adrian Mutu and Juan Vargas after a late-night car crash put the Peruvian's club future in doubt.
Mid-table sides Chievo and Genoa drew 0-0 in Verona.
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