Antonio Conte's side were plunged into the second-tier competition after Galatasaray dumped them out of the Champions League with a dramatic 1-0 group-stage win in December.
That match was played over two days following terrible weather in Istanbul, but first-half goals from Arturo Vidal and Dani Osvaldo ensured a far more comfortable night.
Juventus therefore wrapped up the tie 4-0 and booked a meeting with Serie A rivals Fiorentina in the next round.
With the final set to be held at the Juventus Stadium, the Bianconeri are favourites to win the competition and quickly underlined just why that is the case.
Mauricio Isla hit a post inside the first five minutes with an angled drive that flicked off goalkeeper Onur Kivrak before Federico Peluso had a goal ruled out for offside.
It was no surprise when Vidal fired Juve ahead on 18 minutes.
Osvaldo turned the ball back for Sebastian Giovinco and while his close-range effort was blocked by Kivrak, the ball fell for Vidal to slam home from a couple of yards.
Vidal had the ball in the net again shortly after, only for a close offside call to go against him.
It hardly mattered as Juve's wave of attacks was rewarded with a second goal on the half-hour.
Giovinco ran on to a pass over the static defence and hooked a cross back across the six-yard box for an unmarked Osvaldo to head in.
Juve were guilty of trying to run the ball into the net for the rest of the half and, after the break, their minds had apparently turned to this weekend's league trip to AC Milan.
A lacklustre 45 minutes went goalless, with Peluso missing a glorious chance late on after Kivrak had blocked a Giovinco long-ranger.