Nigel Adkins' men were outclassed by the Serie A side, with veteran striker Antonio Di Natale the star of the show at St Mary's.
The 34-year-old Italian national team forward put the visitors in front after 12 minutes, rifling an unstoppable 25-yard shot into the top corner.
He then set up teammate Willians in the 24th minute, with the Brazilian producing a strike of equal quality from even further out to give Kelvin Davis no chance in goal. Jason Puncheon forced a good save from Zeljko Brkic shortly afterwards, but Di Natale pounced again, volleying home sublimely from close range after Dusan Basta had nodded back a cross from the left into his path. Puncheon flashed a shot just wide of the far post five minutes after the interval, following neat play from Adam Lallana and half-time sub Steven Davis.
But Udinese's fourth arrived in the 64th minute, as Di Natale worked space in the box and slid the ball in to Luis Muriel, who spun and swept home.