Second-half goals from Bruno Fernandes and Cyril Thereau cancelled out Mauro Icardi's opener to give Andrea Stramaccioni a 2-1 victory on his return to his former club
Udinese coach Andrea Stramaccioni returned to haunt his former employers as he faced off against Inter for the first time since being sacked in May 2013.
After a slow start to proceedings, Inter took the lead on the brink of half-time as Mauro Icardi marked his recall to the XI by netting his eighth goal of the season.
However, Inter failed to build on their advantage and the visitors punished them with a sumptuous volley from Fernandes.
Having coughed up the lead, Inter were the architects of their own downfall as Rodrigo Palacio's poor backpass led to Udinese's second goal, with Thereau stealing in to take full advantage.
The win moves Udinese into eighth place in the league table, in the midst of a congested fight for European spots.
The hosts remain 12th after their failure to come back from behind resulted in a third game in Serie A without a win since Roberto Mancini's return to the dugout.
Inter made most of the running in the half but their play in the attacking third lacked a clinical touch, with Palacio and Gary Medel both failing to find a team-mate when in promising positions.
Mateo Kovacic hit the crossbar as Inter edged closer to the opener, but Antonio Di Natale ought to have done better with Udinese's first clear sight of goal after Andrea Ranocchia lost possession, but the veteran striker fired over.
After wasting a handful of promising openings, Inter finally found a way through in the final minute of the first period as Fredy Guarin played a measured throughball to Icardi and the striker calmly fired under Udinese goalkeeper Orestis Karnezis.
The visitors slowly began to get into the game after the interval and Di Natale twice went close with long-range efforts.
And their momentum was rewarded on hour mark as Fernandes fired a superb volley across Handanovic to level things up.
Things went from bad to worse for Inter as they gifted Udinese the winning goal just 11 minutes later.
Palacio under-hit a backpass that allowed Thereau to steal in, round the goalkeeper and roll the ball into the net.
Udinese were made to work for their win with Guarin and Kovacic seeing efforts charged down by a resilient visiting defence.