Willy Caballero was the shootout hero as Chelsea booked a home clash against Newcastle.
Last year’s runners-up were taken to the limit by the Championship side before Caballero saved Nelson Oliveira’s shootout penalty to crush Norwich’s resistance despite having Pedro and Alvaro Morata sent off.
The game appeared to be over thanks to Michy Batshuayi’s second-half goal but defender Jamal Lewis stunned Chelsea with a stoppage-time goal as Norwich took the Premier League champions to extra-time.
The 19-year-old headed home with just 20 seconds left on the clock to leave Daniel Farke, his backroom staff and the Canaries’ travelling fans delirious.
West Ham boss David Moyes was in the stands to run a personal check on Batshuayi, the man that the Blues would be willing to trade for Andy Carroll.
The Belgian showed what he is capable of 11 minutes into the second-half, sneaking into the six-yard box to tuck away Kenedy’s cross.
It will be quite something if Chelsea press ahead with another of their eye-catching transfer moves – trading a goalscorer who has regularly baled out Antonio Conte for a target man who struggled with injury.
Batshuayi was the man who spared Conte’s blushes away to Atletico Madrid this season. He stood up to be counted home at to Chelsea in October as the Blues fought back from 2-1 down. He was the man whose goal last season clinched the title at West Brom.
Yet Conte simply doesn’t fancy him. Any World Cup hopes that Batshuayi has hinge on him getting fixed up soon.
The goal drought for Chelsea, last season’s finalists, began in the original tie between these two sides at Carrow Road on January 6.
Since then Chelsea have failed to justify favouritism against both Arsenal and Leicester, drawing a blank both times.
Here they were awful. Yes there were nine changes from the side held by the Foxes in the Premier League at the weekend.
Even after the goal Norwich winger Josh Murphy hit the post from inside the Chelsea box. The first of a couple of occasions on which the back door was left swinging open by the Blues.
Up front, Danny Drinkwater and Kenedy both missed with opportunities inside the first ten minutes.
Willian looked set to break the deadlock two minutes after that, ghosting into the Norwich box to meet Cesar Azpilicueta’s ball over the top. But the Brazilian bizarrely volleyed wide with the keeper to beat. It was as if the Blues team had been exposed to Kryptonite.
Canaries keeper Angus Gunn held a free-kick from David Luiz comfortably in the 13th minute. Gunn pushed a screamer from Drinkwater onto the bar – superbly it has to be said.
Kenedy was then lucky to escape without card after lashing out at forward Nelson Oliveira.
The incident – right under the linesman’s nose – came after the pair had clashed on the touchline.
Batshuayi opened the scoring after the break but reserve keeper Willy Caballero was still forced to pull off a superb, 64th-minute save to preserve the lead before conceding in stoppage time