Chelsea left-back Kenedy broke the deadlock after a mere 39 seconds to score the fastest goal of the Premier League season on his full Blues debut.
Spain international Diego Costa doubled the west London side’s lead against the Canaries to put Guus Hiddink’s side in control on the stroke of half-time.
Norwich forward Cameron Jermone was denied by the woodwork in the second half before Nathan Redmond netted what ultimately proved a consolation goal for the hosts.
The defending Premier League champions are unbeaten in domestic competitions since Hiddink took over the reins from Jose Mourinho in December.
Chelsea are in eighth place and eight points behind fourth-placed Manchester City, who have played two games less than the Premier League holders.
Chelsea trio Cesar Azpilicueta, Thibaut Courtois and Cesc Fabregas all took to Instagram to post their thoughts on the win on Tuesday night.
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