Antonio Di Natale started and finished the scoring for the Bianconeri, with Citadin Eder giving the visitors hope with an equaliser in the 39th minute.
Kwadwo Asamoah and Dusan Basta scored the home side's other goals in the second half as Cesena struggled with 10 men following the dismissal of Maurizio Lauro on the hour mark.
The win took Udinese top of the league for the time being, but with Milan and Juve in action against Atalanta and Lecce respectively later in the day.
Di Natale has been told by Italy coach Cesare Prandelli that a place in his squad for Euro 2012 can be his if he can carry on scoring, and he wasted no time in opening his account for the new year.
Less than a minute was on the clock when he put Udinese in front after receiving the ball in space at the far post from Antonio Floro Flores' cross as the pair both beat the Cesena offside trap.
The two Udinese forwards combined again in the 13th minute with Floro Flores lifting a delightful ball over the Cesena defence, but Di Natale was unable to get power or direction on his header from eight yards.
Cesena started to respond, with Antonio Candreva testing Samir Handanovic from 25 yards after a few minor scares inside the Udinese penalty area.
They levelled in the 33rd minute with a bit of luck in the build-up to Eder's first goal for the club.
Maurizio Lauro's cross hit the crossbar and fell to Luca Ceccarelli, who headed the ball back across goal for Eder to sweep in on the turn.
Udinese regained the lead in the 54th minute with a speculative effort from Asamoah from 20 yards which squirmed under the body of Francesco Antonioli, the oldest player still in action in Serie A.
Antonioli, who turns 43 this year, will not be keen to see replays of his attempt to keep out the Ghanaian's first Serie A goal of the season.
Lauro was sent off for a second yellow in the 61st minute, complicating matters for Cesena and leaving them with little choice but to see out the remaining half an hour without suffering any further damage.
They failed to do so, with Basta making it three with a 25-yard shot which again left question marks about Antonioli's reactions.
And Di Natale rounded off the victory in the 82nd minute as he picked his spot in the corner beyond the reach of Antonioli, who could not really take any blame for Udinese's fourth and final goal.