Three straight draws had slashed their advantage at the top but their famed resilience coupled with some fantastic play kept the champions four points above second-placed AC Milan, who beat Atalanta 3-1.
Inter were without the suspended Walter Samuel, Ivan Cordoba, Esteban Cambiasso and Sulley Muntari following last weekend's fiery 0-0 draw with Sampdoria and had coach Jose Mourinho banned from the bench.
Midfielder Thiago Motta was forced to play in central defence and Kenya winger McDonald Mariga was handed a first start while struggling Samuel Eto'o was still only a substitute.
Udinese, four points above the drop zone, had a great start when Simone Pepe rifled in after Antonio Di Natale's pass but Inter were soon level thanks to Mario Balotelli's angled shot from the edge of the area on six minutes.
Right-back Maicon then put the visitors 2-1 up after a fine move midway through the first half and Diego Milito, who grabbed the opener in the midweek Champions League win over Chelsea, headed the third just before the break.
Serie A top scorer Di Natale scored a penalty early in the second period after a handball to set up a nervous finale.
ROMA DRAW
Milan fought off relegation-threatened Atalanta at the San Siro after Alexandre Pato's first-half double but the striker went off with a thigh injury and is a big doubt for next Saturday's game at AS Roma.
The Brazilian produced a neat turn and finish on the half hour before converting Ronaldinho's pass 11 minutes later. Jaime Valdes netted for the visitors after the interval but Marco Borriello was quick to restore Milan's two-goal advantage after Ronaldinho's penalty was saved.
Injury-hit Roma in third slipped seven points behind Inter after surrendering a 2-0 lead to draw 2-2 at Napoli, who equalised through Marek Hamsik's stoppage-time penalty.
Palermo surged up to fourth after Fabrizio Miccoli curled in on the hour to set up a 2-0 win at former club Juventus, who lost for the first time under Alberto Zaccheroni and are level with Napoli in fifth with less than a third of the season to go.
A dreadful defensive mixup allowed Igor Budan to walk in the second against a Juve side reminiscient of the demoralised team which Ciro Ferrara left when he was sacked in January.
Genoa missed the chance to move level with Juve when they were beaten 4-3 at home by strugglers Bologna, who triumphed thanks to Adailton's hat-trick, while Sampdoria's push for the fourth Champions League qualifying spot was hit by a 1-0 loss at Parma.
Mid-table Chievo overcame Cagliari 2-1 while bottom side Siena boosted their outside hopes of avoiding the drop with a last-gasp 2-1 win at relegation rivals Livorno in the Tuscan derby.
