Mario Stanic headed Chelsea into an early lead before two goals in seven second-half minutes from Frank Lampard and Gianfranco Zola ended the tie, with substitute Mikael Forssell rounding off an easy win in the dying minutes to earn Claudio Ranieri's side a London derby at Stamford Bridge with The Hammers next Saturday in the 4th round.
Chelsea were still without the injured Jimmy Floyd Hasselbaink, while William Gallas replaced the suspended John Terry in defence.
That was the only change to the Chelsea side that were held to a draw at Bolton last Saturday, while The Canaries made two changes to the side that started at Manchester City on Sunday, with Daryl Sutch and Marc Libbra coming in for tne injured Adam Drury and David Nielsen, still ineligible.
The home side started strongly, with Eidur Gudjohnsen lobbing just over the bar from Zola's pass, before Robert Green saved well from Gudjohnsen's drive and then from Zola's header.
It took Chelsea 11 minutes to take the lead when Zola's corner was headed goalwards by Stanic off Darren Kenton's shoulder. Lampard raised his foot to toe the ball into the net, but he missed and nearly got Green in the face instead, eventually kicking him on the upper chest, causing Green to take his eye off the ball, which sailed on oblivious into the net. The goal should have been disallowed for thefoul on Green, and if it had been then maybe the result would have been different.
The Londoners continued to dominate, with Gudjohnsen firing over, Lampard seeing a 30-yard shot palmed over by Green, and Stanic volleying over before a Graeme Le Saux drive was comfortably handled by Green.
The Canaries were getting back into the game and finally getting some possession - our first good chance came on the half hour mark when Alex Notman's header came back off the bar, but the striker was ruled marginally offside.
Unfortuantely Rob Green was at fault for our second goal - he failed to hold Stanic's dipping 25-yard drive and Lampard knocked home the rebound.
Seven minutes later, Le Saux's corner was met at the near post by an audacious back-heeled flick from Zola to make it three, in what was surely one of the best goals we'll see this year.
Substitute Mikael Forssell was denied by a good block from Green before the Finnish striker fired wide, although he wasn't to be denied a goal, and in the dying minutes he collected Sam Dalla Bona's pass to fire past Green, with the Canaries' keeper palming the ball into the back of the net.