Callum Wilson’s second-half penalty was enough to give Newcastle the points at St James’ Park.
Wilson converted from the spot after keeper Mark Flekken had brought down Anthony Gordon inside the area.
Earlier, Flekken made first-half saves after Aaron Hickey went close for the Bees in the opening few minutes of the game.
Flekken used his feet to deny an unmarked Bruno Guimaraes following a corner, before diving to push away a driven Harvey Barnes cross as Gordon and Wilson closed in on goal.
Newcastle piled on the pressure after the break and eventually broke the deadlock.
The result leaves Brentford 10th in the table after their first five matches of the campaign.
Brentford: Flekken, Hickey (Lewis-Potter 82), Collins, Pinnock, Mee (Maupay 72), Henry (Roerslev 41), Jensen, Norgaard (Onyeka 72), Janelt (Schade 72), Mbeumo, Wissa
Subs not used: Strakosha, Zanka, Yarmolyuk, Ghoddos.