Two first-half goals by schoolboy Islam Feruz condemned the young Canaries to defeat in their FA Premier Academy League match.
The in-form Blues recorded their fourth straight victory at Cobham training centre, taking a 23rd-minute lead through Feruz.
Ten minutes later, he doubled Chelsea's advantage and left the Canaries with an uphill task.
City's best opening fell to Josh Murphy, who scored a hat-trick against Dereham Town in the Norfolk Senior Cup in midweek, but the youngster was unable to finish after going through one-on-one with the Chelsea 'keeper.
City next face Ipswich in a derby at Colney on Saturday (11am).
• Norwich City Under-18s: Matthews, Florence, McFadden, McKenzie, Barker, Kelly, Clunan, McGeehan, Hall-Johnson, Josh Murphy, Jacob Murphy. Subs: Cable, Loza, Norman, Lokko, Carroll.
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