Canaries boss Daniel Farke made 10 changes to the team beaten heavily at Manchester City on Saturday, handing Tzolis and Manchester United loanee Brandon Williams their first outings while giving a full debut to former Werder Bremen forward Sargent.
Greek winger Tzolis was a threat throughout, opening the scoring via a heavy deflection off Cherries defender Zeno Ibsen Rossi.
Full-back Williams, who completed his loan move from Old Trafford on Monday, was involved in Norwich’s second, linking up well with Kieran Dowell in the build-up to McLean’s long-range drive into the top right corner.
Rupp’s composed finish from a Tzolis pass gave the Canaries further breathing space, before Sargent netted his first after Bournemouth goalkeeper Orjan Nyland had parried McLean’s goalbound effort into the forward’s path.
The hosts added a fifth when Sargent capitalised on Nyland’s wayward pass to tee up Tzolis, who then returned the favour for the American to complete the scoring.
Bournemouth beat Norwich en route to the 2018-19 quarter-finals, but registered just one shot on target in the 90 minutes as debutant Brennan Camp sent a tame header straight at goalkeeper Angus Gunn.
Norwich manager Daniel Farke: “It is important that you deliver a good performance, but we also have to be a bit careful.
“This was a game on Championship level, top Championship level, and it proves that if we played there then we would probably romp the league again.
“But the Premier League is a different animal and I have to make sure I don’t throw some lads too early into the cold water.”
Bournemouth manager Scott Parker: “I’m disappointed with the three goals we conceded in the second half. The way you lose is important and those three goals were madness, really.
“I don’t want to apologise but I have the utmost gratitude to the travelling supporters. It was a painful night for them and a painful night for us all.
“It’s very easy [for the fans] to go the other way and leave, but to a man they stayed to support the team. I have nothing but respect for the fans tonight.”
6ZimmermannBooked at 80mins
21WilliamsSubstituted forGiannoulisat 76′minutes
7RuppSubstituted forIdahat 77′minutes
23McLeanSubstituted forGilmourat 71′minutes
44CampBooked at 55mins
26KilkennyBooked at 50mins
7BrooksSubstituted forMephamat 64′minutes
11MarcondesSubstituted forGloverat 64′minutes
27RogersSubstituted forSaydeeat 82′minutes
Match ends, Norwich City 6, Bournemouth 0.
Second Half ends, Norwich City 6, Bournemouth 0.
Attempt saved. Christos Tzolis (Norwich City) right footed shot from the right side of the box is saved in the centre of the goal. Assisted by Adam Idah.
Attempt missed. Christian Saydee (Bournemouth) header from the centre of the box is just a bit too high. Assisted by Brennan Camp with a cross.
Foul by Andrew Omobamidele (Norwich City).
Kyle Taylor (Bournemouth) wins a free kick in the defensive half.
Joshua Sargent (Norwich City) wins a free kick in the defensive half.
Foul by Gavin Kilkenny (Bournemouth).
Attempt saved. Billy Gilmour (Norwich City) right footed shot from outside the box is saved in the centre of the goal. Assisted by Christos Tzolis.
Foul by Christian Saydee (Bournemouth).
Kieran Dowell (Norwich City) wins a free kick in the defensive half.
Attempt saved. Christos Tzolis (Norwich City) right footed shot from more than 35 yards is saved in the centre of the goal.
Corner, Bournemouth. Conceded by Dimitris Giannoulis.
Attempt missed. Christos Tzolis (Norwich City) left footed shot from the left side of the box is close, but misses to the left. Assisted by Adam Idah.
Substitution, Bournemouth. Christian Saydee replaces Morgan Rogers.
Gavin Kilkenny (Bournemouth) wins a free kick in the defensive half.
Foul by Christos Tzolis (Norwich City).
Christoph Zimmermann (Norwich City) is shown the yellow card for a bad foul.
Morgan Rogers (Bournemouth) wins a free kick on the left wing.