Sergi Canos gave the Bees the perfect start after five minutes finishing off a slick five-man move on the edge of the box before Lasse Vibe made it two with a ferocious drive into the roof of the net shortly after.
Alan Judge made it three on the half hour when his free-kick into the corridor of uncertainty flew past everyone into the far corner. But Joe Lolley signalled the visitors’ intent within seconds of the restart only to see the three-goal cushion restored with a hotly contested penalty minutes later.
Ben Chilwell was adjudged to have shoved Judge in the box and the Irishman stepped up to fire home from the spot.
“That was a turning point in the game,” said Terriers boss Wagner. “I was a long way away but the reaction of players on both sides and fans suggested it was not a penalty. In the first half we didn’t pass, lost possession of the ball too easily and had no movement. It was the worst display I’ve seen from us.”
Kyle Dempsey’s late consolation meant his side edged the second half in terms of goals and possession and Wagner added: “The first-half performance was not us but the second half was completely new.
“I told them to go out and show character and show that they are good players... which they did.”
Nahki Wells went close to reducing the arrears three times in the second half.
Brentford: Button, Colin, Dean, Tarkowski, Bidwell, Woods (McEachran 75), Diagouraga, Canos (Saunders 58), Judge, Swift (Jota 80), Vibe. Unused substitutes: Hofmann, McCormack, Bonham, O’Connell.
Huddersfield: Steer, Smith, Hudson, Lynch, Chilwell, Cranie, D Holmes (Dempsey 46), Lolley, Paterson, Carayol (Scannell 61), Miller (Wells 46). Unused substitutes: Davidson, Wallace, Bunn, Allinson.
Referee: P Gibbs (West Midlands).
Man of the match: Lasse Vibe.