After missing key chances in a 2-1 home defeat to Atalanta at the weekend, Inter suffered again in front of the San Siro fans to leave themselves vulnerable in fifth place.
They dominated in possession, but had just a handful of chances, the best of them late on when Esteban Cambiasso's powerful shot was palmed clear and Maurizio Domizzi acrobatically blocked Danilo D'Ambrosio's header on the rebound.
Indeed, it seemed just as likely that they might be caught on the break, with Udinese having the best chance of a drab first half when Bruno Fernandes saw a drilled effort well saved by ex-Udinese goalkeeper Samir Handanovic before Inter's defence scrambled clear a follow-up effort from Emmanuel Agyemang-Badu.
Inter had been restricted to long-range efforts, but Fredy Guarin - disappointing just days after signing a new deal with the club - and Rodrigo Palacio missed the target.
Visiting goalkeeper Simone Scuffet had more to do in the second half, pushing clear Andrea Ranocchia's effort early on, but it was not until after the hour mark that Inter showed enough to have the home supporters believe a breakthrough was coming.
Palacio turned inside the area to fire in a shot Scuffet did well to clear before the goalkeeper stretched to keep out a Hernanes effort from the edge of the area.
Walter Samuel and Palacio eached wasted free headers while Mauro Icardi somehow cleared the crossbar from close range, but Udinese's goal was living a charmed life and after Domizzi got back to block D'Ambrosio's header, they could be sure of a point.