Maurizio Sarri, who watched his side top Serie A on Sunday, rang the changes with Cristiano Ronaldo, Blaise Matuidi, Miralem Pjanic, Juan Cuadrado and Wojciech Szczesny missing out.
Gonzalo Higuain broke the deadlock on 16 minutes after exchanging passes with Paulo Dybala before bringing the delivery under control for a cracking finish past Nicolas.
Juve were just getting started and a Video Assistant Refereeing review earned the side a penalty after Nicolas brought down Federico Bernardeschi, as Dybala fired home on 26 minutes.
Udinese made a change after halftime, unleashing the big guns in Kevin Lasagna with Lukasz Teodorczyk making way.
The Old Lady continued dominating as Higuain netted a second on 54 minutes with a simple tap-in from a rebound by Nicolas, but it was disallowed for offside by VAR.
There was no denying Dybala three minutes later after the Argentine curled Higuain's layoff into the top left-hand corner to give the Bianconeri an unassailable lead.
Another penalty went to Juve on 61 minutes following a handball in the area by Bram Nuytinck. Douglas Costa stood forward to fire home the spot kick.
Sarri's outfit were in search for more, but a powering header from Daniele Rugani came off the outside post following a free-kick, as Juve march to the last eight with reasonable ease.