The 38-year-old faced off against Inter for the first time since being sacked in May 2013 and his current employers came from behind to grab all three points thanks to goals from Bruno Fernandes and Cyril Thereau.
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, 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.
However, the hosts remain 12th after their failure to fight back resulted in a third game in Serie A without a win since Roberto Mancini's return to the Inter 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 half as Fredy Guarin played a measured throughball to Icardi and the striker calmly fired under Orestis Karnezis.
Udinese slowly but surely began to get into the game after the interval and Di Natale twice went close with long-range efforts, the second well saved by Handanovic.
And the visitors' building momentum was rewarded a minute before the hour as Fernandes teed himself up before firing a superb volley across Handanovic to level things up.
Things went from bad to worse just 11 minutes later for Inter as they gifted Udinese the winning goal.
Palacio played an under-hit back pass towards Handanovic 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.
And Stramaccioni was to hold out for a notable victory against his former club, who sit nine points off the top three as Mancini's Inter comeback fails to take flight.
