Lazio midfielder Marco Parolo had nodded in the first goal from a curling Andreas Pereira cross on 23 minutes in the last-16 tie.
Parma dropped to 18th position into the relegation zone after their fourth consecutive defeat 3-0 against Atalanta midweek.
Juventus had to play most of the match at a numerical disadvantage after former Fiorentina winger Juan Cuadrado was sent off in the 18th minute.
Serie A: Cristiano Ronaldo's twin strike helps Juventus inflict 4-0 loss on Parma, inch closer to leaders AC Milan
Ronaldo, who missed a penalty in the midweek 1-1 draw with Atalanta, made amends with his third brace in four games.
European football matchday: Liverpool look to remain an top as they take on Crystal Palace; Barcelona host Valencia
After beating Tottenham 2-1 on Wednesday night to go top, Liverpool is away to Crystal Palace in a lunchtime kickoff — barely 62 hours later.
Serie A: Theo Hernandez brace helps AC Milan secure 2-2 draw against Parma; Inter Milan move to second spot
Nicolò Barella, Danilo D'Ambrosio and Romelu Lukaku scored in the final 15 minutes after Riccardo Sottil had given Cagliari the lead shortly before halftime.
Antonio Conte's side are second in Serie A, five points behind leaders AC Milan, with the two city rivals trying to deny Juventus a 10th consecutive league title.
Serie A: Neither coach on sidelines as Torino, Sampdoria share spoils; Gervinho's brace helps Parma beat Genoa
Neither coach was on the sidelines as Torino and Sampdoria drew 2-2 in Serie A. Meanwhile, Gervinho scored twice to help Parma beat Genoa 2-1.
Serie A: Ageless Ibrahimovic's brace helps AC Milan beat Napoli; Inter Milan come from behind to defeat Torino
Zlatan Ibrahimovic scored twice to raise his total to 10 goals in six games played as Milan won 3-1 at Napoli on Sunday.
Serie A: Joao Pedro matches Italy legend Riva's 52-year Cagliari record, M'Bala Nzola brace lifts Spezia
Sampdoria and Cagliari are 10th and 11th respectively, both on 10 points after seven games, as they push for European football next season.
Serie A: Inter Milan left furious by contentious VAR decision during draw against Parma; Atalanta beat Crotone
Inter had a strong penalty appeal when Botond Balogh hauled down Ivan Perisic in the second half, with Conte skipping his press conference, apparently in protest at the decision.
Darmian will be on loan until the end of June at which point he will join Inter on a permanent deal with the fee reported to be 2.5 million euros ($2.9 million).
Serie A: Atalanta ease past Cagliari with a 5-2 victory; Inter Milan settle for 1-1 draw against Lazio
Inter Milan dropped their first points of the season as they drew 1-1 against Lazio in Serie A while Atalanta made it three wins out of three with a 5-2 victory over Cagliari.
Serie A: Juventus cruise past Sampdoria to get off to dream start under new boss Andrea Pirlo; Napoli beat Parma
The match was played in front of 1,000 spectators as Serie A stadiums reopened on Sunday to a limited number of fans after a seven-month coronavirus lockdown.
Ruslan Malinovskyi and Alejandro “Papu” Gomez scored in the second half after former Atalanta midfielder Dejan Kulusevski had given Parma the lead.
Serie A: Romelu Lukaku scores brace as Inter Milan beat Genoa to stay in title race; Napoli earn win against Sassuolo
Both Inter and Genoa were desperate for the points but chances were few and far between.
Serie A: Inter Milan's draw against Fiorentina takes Juventus one step closer to title; Parma beat Napoli
Romelu Lukaku and Alexis Sánchez each hit the woodwork for Inter, who also had a potential goal from Antonio Candreva waved off for offside.
Serie A: Parma's entire squad test negative after staff member's positive COVID-19 result in previous test
It was first the positive case at a Serie A club since the league restarted on 19 June following a three-month stoppage.
Serie A: Juventus goalkeeper Gianluigi Buffon overtakes AC Milan's Paolo Maldini to set league appearance record
Buffon joined the Bianconeri in 2001 after starting his career with Parma and swiftly established himself as one of the best goalkeepers in the world.
Serie A: AC Milan pay tribute to coronavirus victims in 2-0 win over AS Roma, Inter come from behind to beat Parma
AC Milan are in seventh place while AS Roma remained fifth and dropped nine points behind Atalanta, which beat Udinese 3-2 and holds the final Champions League spot.