Kenny McLean pulled one back in the 87th minute to halt Thomas Frank's sides impressive form.
Ivan Toney opened the scoring with right footed shot from very close range in the 27th minute of the game.
But McLean scored in the later stages of the game with a left footed shot from outside the box to the bottom left corner to make it 1-1.
MATCH FACTS
Brentford: Raya, Dalsgaard, Pinnock, Bech Sorensen, Henry, Marcondes, Jensen, Dasilva, Mbeumo, Toney, Ghoddos
Substitutes: Thompson, Goode, Canos, Forss, Fosu-Henry, Janelt, Daniels
Norwich: Krul, Aarons, Hanley, Gibson, Lungi Sorensen, Skipp, Rupp, Buendía, Vrancic, Cantwell, Pukki
Substitutes: Hugill, Placheta, Stiepermann, McLean, Tettey, McGovern
Referee: Jeremy Simpson
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