Dusan Vlahovic scored the first goal in the opening half, while Teun Koopmeiners sealed the victory for the 15-time winners with an incredible long-range free-kick in the last-16 tie.
Francisco Conceicao and Nico Gonzalez netted late to underline an emphatic performance by the Old Lady.
"It was a good performance," Juve coach Thiago Motta told Canale 5.
"These lads are going through a tough situation in the right way, giving their all in every training session," he added of his players who have endured a stop-start domestic campaign as they sit sixth in the league table.
Juve join Lazio, Empoli, Bologna and AC Milan in the next stage of the cup.
Serie A leaders Atalanta are in action on Wednesday against Cesena, while Roma take on Sampdoria.
Reigning Scudetto champions Inter Milan complete the round of 16 when they host Udinese on Thursday.
In Turin, Vlahovic put the home side in front one minute before half-time when he swivelled smartly on a pass to feet from Kenan Yildiz and rolled the ball into the far corner.
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Summer signing Koopmeiners then notched up his second goal for Juve with an unstoppable left-footed free-kick from 25 metres out in the 53rd minute.
Vlahovic had the ball in the net twice more for Juve as they pressed forward in search of a third, but was on both occasions denied by the assistant's flag for offside.
Conceicao eventually made it three on 80 minutes with a whipped finish after cutting in from the right flank and Gonzalez chipped home a fourth with one minute remaining.
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