Emanuele Giaccherni drew first blood for the Turin giants and veteran forward Alessandro Del Piero doubled his side's lead after half an hour.
Roma imploded when forward Erik Lamela was dismissed in the second half and their misery was completed thanks to an own goal from defender Simon Kjaer in stoppage time.
Juventus honcho Conte revealed after the final whistle that his troops were hungry for the victory.
"We wanted to get through to the semi-finals to get us reacquainted with fighting for important goals," Conte was quoted as saying on the club's official website.
"Today we made seven changes from Saturday's starting line-up. I opted for the side that would give me the best guarantees, picking those who have played less but who have always responded in an excellent manner."
Conte paid tribute to several of his unheralded squad players after they pressed their claims for a regular spot in the team.
"(Luca) Marrone is an example of this, a 20-year-old youngster who's deserving of high regard. But I'm also happy about (Marco) Storari's test, how (Marco) Borriello stepped in, (Marcelo)Estigarribia's extraordinary display and naturally Del Piero's response", Conte purred.
"The lads are all in good condition and I need to compliment my staff for this."