Arturo Vidal gave the champions a 14th minute lead from the penalty spot before Mirko Vučinić doubled their advantage on the stroke of half-time with smart finish from the edge of the area.
Sebastian Giovinco then grabbed a second half double before Andrea Lazzari scored a late consolation for the home side.
Udinese were without Odion Ighalo and Paulo Barreto through injury for the visit of Juventus as they attempted to recover from the dual disappointment of their opening day defeat against Fiorentina and the penalty shoot out loss to Braga in Champions League play-off in midweek.
In spite of the uncertainty regarding the future of manager Anontio Conte, Juventus’s opening day 2-0 victory over Parma extended their unbeaten run to 40 games and they welcomed back goalkeeper Gianluigi Buffon and defender Giorgio Chiellini to their squad after both recovered from injury for the trip to Udine.
Massimo Carrera has proved a steady hand in the absence of Conte on the touchline and their task was made all the more easier with a little under a quarter of an hour gone when indecision got the better of Brkić as Andrea Pirlo lofted a trademark pass over the defence.
The Serbian first hesitated before electing to meet the through ball. The moment’s hesitation proved costly though as it offered Giovinco a window to get his head to the ball before the keeper’s momentum upended the diminutive forward.
Vidal made no mistake from the spot to increase the task ahead of Francesco Guidolin’s men, who were down to ten men as the referee deemed the challenge from Brkić as preventing a clear goal scoring opportunity.
The hosts remained compact as they looked to frustrate their visitors. Their resolve was admirable but the numerical disadvantage meant that whenever they did manage to win the ball back they were a relatively blunt attacking force.
Their likeliest avenue back into the game looked to be through set-piece situations but with the delivery all too often letting them down it looked like they were to go to the interval with a one goal disadvantage.
However, with the half into added time, the hosts were to pay a heavy price for a collective loss of concentration as Kwadwo Asamoah found Vucinic unmarked on the edge of the area. The forward opened his body and curled the ball around substitute keeper Daniele Padelli to put his side into a two goal lead.
That late first half goal completely changed the complexion of Guidolin’s half-time team talk, and, in truth, put the tie beyond the men from Udine.
But, credit to the hosts, they began the second half with intent but their hopes of getting anything from the game were all but extinguished when the busy Giovinco was first to react to a Claudio Marchisio parried effort to give the visitors a three goal cushion.
With Guidolin’s men tiring, Pirlo slipped a ball into the channel for Giovinco to add a fourth with a smart finish across Padelli from just inside the box.
Despite falling a further goal behind, the hosts showed great character to muster some territory and possession in the latter stages of the half.
Lazzari converted that territory and possession into a well deserved consolation goal when he capitalised on a lapse in concentration in the Juventus defence to bundle the ball past Buffon with a little over ten minutes remaining.
The result compounds what has been a difficult start to the season for the Guidolin’s men but the resolve shown against last year’s champions will hold them in good stead for the season ahead.