First-half goals from Rodrigo Palacio and Andrea Ranocchia gave Walter Mazzarri's men a comfortable advantage they would not relinquish.
Fredy Guarin was denied by the woodwork as Inter went in search of a third and it duly arrived in the 91st minute, with Ricky Alvarez tapping home to consign Udinese to their third defeat in four matches.
Both sides made two changes from their midweek fixtures. Emmanuel Agyemang-Badu and Silvan Widmer returned for Udinese, while Ranocchia and Saphir Taider came back in to the starting XI for Inter.
After a quiet opening 20 minutes, Mazzarri's men twice went close to breaking the deadlock in the space of 60 seconds.
First, Cambiasso won the ball 30 yards from goal before unleashing a fierce drive that was tipped over the crossbar by Zeljko Brkic, then Jonathan played a clever ball in to Yuto Nagatomo, who snatched at his effort from six yards and sent the ball wide.
Inter did not have to wait long to take the lead, however, as Palacio rose highest to nod home Taider's right-wing free-kick from seven yards in the 25th minute.
The advantage was doubled four minutes later, Ranocchia volleying home Esteban Cambiasso's left-wing corner into an empty net after Brkic had misjudged the flight of the ball as he attempted to come and collect.
Udinese should have been back in the game 10 minutes before the break, Luis Muriel capitalising on a terrible mistake by Walter Samuel before dragging his angled effort horribly wide, the ball running out of play for a throw-in on the far side.
The home side began the second half strongly, former Udinese goalkeeper Samir Handanovic produced a spectacular save to deny Antonio Di Natale's dipping effort two minutes after the restart before Maurizio Domizzi sent an overhead kick narrowly wide 10 minutes later after Inter struggled to clear a ball into the box.
Despite Udinese's greater threat in the second half, it was the visitors who went closest to grabbing the next goal in the 61st minute, Guarin powering past Domizzi in the box before seeing his low effort cannon off the base of Brkic's right-hand post and away to safety.
Inter did indeed claim a third goal in stoppage time, Palacio squaring the ball for Alvarez to slot home into an empty net as the visitors closed out a win that took them to within six points of Juventus in the final Champions League qualification berth.