Second-half goals from Gokhan Inler and German Denis left second-placed Napoli, chasing their first scudetto since Diego Maradona's days in 1990, six points adrift of leaders Milan with five matches to play.
Napoli striker Edinson Cavani, the championship's second top scorer with 25 goals, missed a penalty in a bad-tempered game featuring several flare-ups, although only Udinese's Maurizio Domizzi was sent off.
Milan, 3-0 winners over Sampdoria on Saturday, have 71 points from 33 games with Napoli stuck on 65 and Inter Milan, champions for the last five seasons, on 63 after their 2-0 defeat at Parma on Saturday.
Juventus were left facing a second successive season without Champions League football after they were held 0-0 by Fiorentina in a dour affair while rivals Lazio thrashed Catania 4-1.
Those results left Juventus eight points adrift of Lazio who are in fourth place, the Champions League qualifying round berth, with 60 points.
Seventh-placed Juve will have to concentrate on finishing fifth or sixth to qualify at least for the Europa League.
CAVANI OFF-TARGET
Cesena moved out of the relegation places with a 1-0 win over bottom club Bari thanks to a second-half goal from 34-year-old Albania striker Erjon Bogdani.
Cesena's win sent Sampdoria, whose bus was pelted with sticks and stones by their own fans on returning to Genoa on Saturday, into the danger zone in their place.
Napoli, winners of their last four league games, took early control with Cavani twice going close but it fell apart for them in a six-minute spell after the break.
Switzerland captain Inler, a Napoli transfer target, opened the scoring with a swerving, deflected 25-metre shot in the 55th minute to stun the San Paolo stadium.
Udinese coped well without injured first choice strikers Antonio Di Natale and Alexis Sanchez when Pablo Armero burst down the left and crossed to the far post where Denis chested the ball down to fire the second against his former club.
Tempers flared several times after that, on one occasion after an Udinese player went down injured and Napoli played on.
There was another scuffle after Napoli were awarded a penalty in the 87th minute, ending in a red card for Domizzi.
After a two-minute delay, Uruguay forward Cavani saw his kick saved by Samir Handanovic.
Brazilian midfielder Hernanes gave Lazio a 40th-minute lead at Catania following a headed pass from Stefano Mauri.
Matias Schelotto levelled straight after the break but Mauri put Lazio back ahead in the 56th before late goals from Sergio Floccari and Argentine Mauro Zarate completed an impressive win.
At the bottom, Cesena's win lifted them to 17th, one place above the danger zone, with 34 points, two more than Sampdoria.
Bari stayed rooted to the bottom of the table with 21 point
