Attacking midfielder Ollie Watkins was in great form as he scored one and created another with Brentford dominating large chunks of the game despite falling behind.
Norwich open scoring before Brentford strike back
Playing behind closed doors at Norwich's London Colney training base, Brentford threatened with a handful of attacks before Norwich took the lead through a piece of quality within the opening ten minutes. Onel Hernandez worked some space before Emi Buendia curled a wonderful effort into the bottom corner from just outside the penalty area.
Yet Brentford, who will be hunting down a playoff place this season, responded immediately with former Norwich player Sergi Canos pulling the strings in midfield. It was the Spaniard who released Emiliano Marcondes with a perfectly weighted ball between the Norwich defence before the Dane rounded Ralf Fahrmann and slotted the visitors level.
Brentford found themselves on top for much of the first half as Norwich's defence, including debutant Sam Byram, were forced into several desperate blocks as Canos and Watkins probed, the latter forcing Fahrmann into a smart stop down low.
In contrast, Hernandez appeared to be the greatest threat for the home side down the other end, finding Josip Drmic but the new signing could only head straight at David Raya.
Watkins proves the difference
With Canos replaced at half-time, Brentford lost some of their attacking intensity but even the opposing introduction of Marco Stiepermann failed to pick apart a well-drilled Brentford defence.
At the other end, Watkins went close with a deflected effort but he eventually got a deserved goal on 69 minutes as he guided home a Marcus Forss cut-back.
Left-back Philip Heise forced a good save from a well-struck free-kick as Norwich tried to issue a response but they still found themselves having to put bodies on the line down the other end.
Eventually, the visitors scored a third as Watkins' set-piece caused havoc and Ethan Pinnock prodded home.
As Forss went close late on from another Watkins free-kick, Max Aarons hit the post after clever play from Todd Cantwell before teenager Adam Idah headed wide with seconds left on the clock, Norwich falling short for the first time this summer.