Chelsea struggled against the Canaries, for whom Alex Pritchard, Josh Murphy and James Maddison excelled going forwards.
Given Antonio Conte‘s regular fixture complaints, he would not have wanted a replay, but Championship Norwich frustrated the Blues, who came closest when Willian’s effort was turned round a post by Angus Gunn.
And Chelsea, Premier League champions and FA Cup finalists last season, will now host Daniel Farke’s men at Stamford Bridge in 10 days’ time.
Conte, as promised, rotated his side, with Wednesday’s Carabao Cup semi-final first leg with Arsenal in mind.
David Luiz played his second game since October after a rumoured fallout with Conte and a subsequent knee injury.
The Brazil defender is not the only person to get on the wrong side of Conte this season, with the Italian’s feud with Manchester United boss Jose Mourinho escalating on Friday.
Conte says he is “ready to fight…with everyone”. And he was as animated as ever in his technical area, despite the “clown” comment from Mourinho which the United boss had insisted was self-deprecating, rather than aimed at the Italian.
Norwich troubled their visitors. Murphy’s runs made Antonio Rudiger uncomfortable and Pritchard pounced on two Luiz lapses.
Pritchard stole the ball when Luiz received a Willy Cabellero pass, but his heavy touch saw the ball go out for a goal kick.
Next Luiz’s mis-kick was seized upon by Murphy and Pritchard created a chance, but Luiz recovered to block.
This was not to be as straightforward as Luiz’s last appearance, a 4-0 win over Qarabag in Baku on November 22.
Chelsea were seeking an outlet, but Michy Batshuayi’s control continually let him down, up against imposing pair Christoph Zimmermann and Grant Hanley.
Willian and Pedro, under pressure to perform following the arrival of Ross Barkley, offered little support, while Tiemoue Bakayoko and Danny Drinkwater could not get a foothold in midfield.
Murphy again ran at and beat Rudiger, but appeared caught by indecision as his final ball was neither a shot nor a cross. The ball went out for a throw in.
Luiz was booked for catching Maddison late and Batshuayi made his frustration clear by squabbling with Hanley at half-time.
Batshuayi’s tame effort early in the second half was Chelsea’s first on target. There were plenty off target.
Chelsea’s best chance was fashioned by Willian, but Gunn turned his shot around a post. The goalkeeper held another effort from the Brazilian soon afterwards.
Norwich continued to cause problems and Conte had seen enough.
With 16 minutes remaining Alvaro Morata was on, with Batshuayi withdrawn.
Charly Musonda was also sent on, for Kenedy, but Davide Zappacosta’s stoppage-time volley wide from distance was the closest Chelsea came to breaking the deadlock.
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