Neither side could find the net in the opening 45 minutes.
But the Terriers were in front five minutes after the break via Kachunga.
The Bees equalised with a goal from Yennaris (77), but Palmner restored the hosts’ advantage two minutes later.
Huddersfield: Ward, Smith, Hudson, Schindler, Lowe, Hogg, Mooy,
Lolley, Payne, van La Parra, Kachunga. Subs: Scannell, Coleman,
Cranie, Paurevic, Stankovic, Hefele, Palmer.
Brentford: Bentley, Clarke, Egan, Dean, Elder, McEachran,
Woods, Kerschbaumer, Sawyers, Macleod, Hogan. Subs: Saunders,
Yennaris, Hofmann, McCormack, Bonham, Field, Holldack.
Referee: Geoff Eltringham (Tyne & Wear)