Jose Mourinho’s men made a flying start when Oscar gave them a fourth-minute lead after Demba Ba’s lay-off from Frank Lampard’s lofted pass. Victory from then seemed a formality for Chelsea but it appeared anything but until a late rally.
Ba might have netted early in the second half following a cross from Ramires, who was relieved not to concede a penalty when challenging Anthony Pilkington.
Norwich levelled when Pilkington headed in from close range and had further opportunities, but Hazard finished off a ruthless counter attack, and Willian curled in his first Chelsea goal to complete the win.
There were moments of alarm for England manager Roy Hodgson prior to World Cup qualifiers with Montenegro and Poland.
Canaries keeper Ruddy, who had an opportunity to show he should be England’s number one ahead of Joe Hart, should have done better in two aerial duels with Ba and allowed Hazard’s weak shot to beat him, while Chelsea left-back Ashley Cole departed 15 minutes from time clutching his rib cage.
After the match, Mourinho revealed he “smelt defeat” before making game-changing substitutions with Hazard and Willian in the last 15 minutes.
He said: “During the game I am not nervous. I have feelings. I smell things, and when that easy goal (from Ba) was missed, I had a smell that they would score a goal. That is why I had Eden warming up at 1-0 because I smelled that.
“If they had scored a second goal, we would probably lose, but we are trying to be top.”
Mourinho felt he had to do something to try to turn the game back in his side’s favour, with Norwich dominating for long spells in the second half.
“They come in and they change the game, the manager [Chris Hughton] did very well. If they come on and make it worse, it’s a very bad decision by the manager. It is their responsibility,” the Chelsea manager said.
“The situation had become difficult at 1-1. We all knew that a point here would be a bad result for us, but I think the team coped well with the pressure and, without using totally the balance, we could gamble and risk a bit to try and bring something different to the game to see if Norwich could cope.”
Mourinho acknowledged Norwich had pushed his side, using the strengths of a squad assembled at a fraction of the cost of his own. “It was very British in the sense of the emotion,” he said. “You could feel the crowd waiting for moments of emotion. They were winning a corner and the emotion was coming into the game. They put a long ball in the box to [Ricky] van Wolfswinkel and the noise was pressing for the second man arriving in the box. It is their style adapted to the players’ profile.
“They have this. I don’t have, so I have to go with what I had. I had to put Eden and Willian, all three on, two quick strikers with Eden and (Samuel) Eto’o. We go with what we have.”