The veteran forward struck twice, either side of a fine finish from Luis Muriel, as the Zebrette began the New Year in emphatic style at the expense of Andrea Stramaccioni's side
Antonio Di Natale opened the scoring against the run of play midway through the second half and Luis Muriel doubled the hosts' advantage when he slotted home not long after being hacked down by Juan Jesus, who was shown a second yellow card for his indiscretion.
Udinese then put the seal on a resounding win when Di Natale added his second late on, heaping further misery on struggling Inter in the process, with Andrea Stramaccioni's men now having gone four games without a win in Serie A.
The first real chance of an intriguing encounter fell to Muriel, but his effort was from too tight an angle and comfortably gathered by Inter shot-stopper Samir Handanovic.
At the other end, it was midway through the first half before Inter finally mustered their first shot on goal. An Antonio Cassano corner was headed to the back post by Rodrigo Palacio and eventually found its way to Esteban Cambiasso, who fired his half volley over the bar.
Nerazzurri front-man Palacio was judged to have dived and received a booking following a coming-together with Maurizio Domizzi moments before Di Natale crashed a stunning free kick against the bar, leaving Handanovic rooted to the spot.
Inter again looked to test Zeljko Brkic as Walter Gargano strode forward from midfield. The Uruguayan fired his effort towards the near post, but the Udinese goalkeeper was on hand to tip around the post.
Di Natale had the opportunity to test Handanovic with five minutes of the half remaining from another free kick. However, his strike failed to test the Inter No.1, who saw his curling effort drift over the crossbar before Giovanni Pasquale blasted out for a goal kick from distance.
Inter began the second half the stronger of the two sides and perhaps should have taken the lead five minutes of the restart, Jonathan somehow side-footing wide from six yards out of Brkic's goal when it looked easier to score.
Freddy Guarin then tested the Serbian international from close range, but the Udinese shot-stopper was able to get down low to deny the Colombian, before Palacio saw his effort blocked by Brkic moments later.
Inter continued to dominant proceedings and Palacio perhaps should have done better after some good work by Guarin. The Argentine appeared to slip before firing his effort away and blasted wide.
Moments later, Udinese took the lead, arguably against the run of play. Di Natale was played in behind the Inter defence by Andrea Lazzarri before firing across goal. Handanovic got a hand to his shot, but it was too powerful for his former team-mate as the Italian's effort nestled into the bottom corner.
Things went from bad to worse for the Nerazzurri minutes later after Juan fouled Muriel to receive his second booking of the encounter and was subsequently red carded. Di Natale stepped up to take the free kick, but Handanovic was equal to the striker's effort this time around and held onto the ball well.
However, the Zebrette made their one-man advantage count with 15 minutes to go. Muriel was played in by Dusan Basta and the Udinese striker fired past Handanovic with a goal identical to Di Natale's opener.
Di Natale then netted his second and Udinese's third five minutes later, poking home from close range after being picked out by Lazzarri from the left.
Inter pressed for a late consolation, but were made to rue Jonathan's miss five minutes into the second half as the hosts coasted to an impressive 3-0 victory.