Portugal forward Ronaldo opened the scoring at Allianz stadium along with his seventh goal in four matches for Juve in 2020.
Rodrigo Bentancur and Leonardo Bonucci then found the net to provide the Bianconeri a three-goal advantage at half-time.
Roma force one back once Cengiz Under’s effort from the edge of the box hit the crossbar and rebounded into the net off veteran goalkeeper Gianluigi Buffon, however Juve comfortably advanced and will face Milan or Torino – who meet on January twenty eight – within the last four.
Juventus head coach Maurizio Sarri picked a powerful starting line-up for the quarter-final clash and after a low-keyed start his side increased the tempo to seize control.
The 13-time Coppa italia winners took the lead within the twenty sixth minute with a goal that owed much to Ronaldo’s ability to finish from a good angle.
Ronaldo escaped his marker on the left before cutting within and guiding a coffee shot across goal past Roma keeper Pau Lopez.
Juventus added a second on the counter attack twelve minutes later once Bentancur, encircled by six Roma players, squeezed a shot into the bottom-left corner from twelve yards.
Roma’s defence were culpable for Juve’s third on the stroke of half-time as the unmarked Bonucci sedately headed in at the rear post after being picked out by Douglas Costa’s cross.
Gonzalo Higuain hit the woodwork within the forty eighth minute and Paulo Fonseca’s side reduced the deficit 2 minutes later.
Under’s shot from just outside the box struck the bottom of the bar and went in off Buffon’s hand.
However, Juventus stood firm within the closing stages to pick up a fifth straight victory in all competitions.