The first-half was a relatively unexciting affair as Chelsea dominated with 62 per cent possession, although the visitors grew into the game, finding plenty of spaces on the counter.
Both teams managed to hit the crossbar in the first 45 minutes as a lack of clinical finishing became the theme of the night. For the hosts, Danny Drinkwater struck the bar with the inside of his foot from outside the box in the 25th minute. Norwich's goalkeeper Angus Gunn was clearly beaten but thankfully the woodwork saved him.
That effort appeared to shock the visitors into a response, which largely originated from their Portuguese striker Nelson Oliveira, wo hit the crossbar in the 32nd minute and attempted another shot after breaking free 3 minutes later.
Conte's team were clearly frustrated they couldn't find the breakthrough despite posting 13 shots. Kenedy reacted to a foul from Oliveira in the 39th minute which could have warranted a yellow card if the referee had seen it.
After the break and a lacklustre opening 10 minutes, the hosts finally took the lead through a low cross on the left-hand side by Kenedy who created an easy tap in for Batshuayi from eight-yards out.
However, despite their dominance Chelsea couldn't kill the game off with the hosts surviving a scare when Caballero failed to deal with a lofting ball which eventually found its way to Maddison who could only hit the post.
Morata was arguably the most wasteful even though the Spaniard was only brought on in the 80th minute. He failed to direct a fast cross from the right wing from Drinkwater into the back of the net ot make contact with a cross from Pedro on the other side which was right infront of goal.
The London club would go on to rue these missed chances as an unmarked Jamal Lewis directed a beautiful cross from Klose off the post and into the net to force extra-time. Stamford Bridge was stunned.
- Extra Time -
Extra time followed the same pattern as the game with the hosts being wasteful of numerous chances. Conte had to bring on star-man Eden Hazard to try and force a late winner.
However, the biggest talking point from the night came from the three bookings for diving for Chelsea, which were given to Pedro, Willian and Morata.
Pedro's and Morata's would prove fatal as the two Spaniards picked up second bookings in the last 10 minutes of extra time to reduce the hosts to nine-men with a penalty shoot-out approaching.
Pedro was given a second yellow for a late challenge on Maddison, who was trying to break free on the counter. Nonetheless, Morata's was more rash. After being booked for diving, the 25-year-old persistently gave dissent to the referee who was having none of it and produced a second yellow in a matter of seconds.
- Penalty Shoot-out -
Thankfully the hosts were able to find their finishing in the shoot-out. Despite losing two of their penalty takers to red cards, Chelsea scored all five of their penalties comfortably with Hazard netting the final one. Norwich's Oliveira will take most of the blame after his tame effort was saved by Willy Caballero.
Although the result seems harsh on the visitors, the Premier League leaders deserved to progress to the fourth round, where they will face Newcastle United. However, it was quite the scare for Conte's team who cannot afford to lose their head like that again when they face more clinical opposition.