The home side were dealt a blow 12 minutes into the second half when Germany's Christopher Schindler, who was booked for impeding West Brom striker Hal Robson-Kanu in the first half, got his second yellow for a lunge on defender Ahmed Hegazi.
West Brom responded with a triple substitution, bringing on forward Salomon Rondon and midfielders Matt Phillips and James McClean but Huddersfield maintained their composure at the back.
Yet the hosts had to defend with determination in the closing stages of the game and Danish goalkeeper Jonas Lossl pulled off two sharp saves in the second of six added minutes to deny McClean and Phillips.
The loss, West Brom's third in succession, left them without a win in nine league games to pile pressure on manager Tony Pulis while Huddersfield boss David Wagner celebrated one of his "biggest wins" since taking charge.
"We showed team spirit, fighting spirit and the ability to defend. The game's story makes it one of our biggest wins. The crowd played their part in getting the result... they were unbelievable again," Wagner said.
"The players had a long way to go after the red card, but showed a proper 'Terriers' reaction... We kept West Brom away from goal for as long as possible, but when we needed him Jonas Lossl made two world class saves."
Huddersfield, who beat second-placed Manchester United 2-1 at the John Smith's Stadium last month, have recorded successive top-flight home wins for the first time since 1971.
"Today was one of the highlights of my two years here. The players totally deserved the win," said Wagner.
Huddersfield, who climbed to 10th in the table and have 15 points from 11 games, will travel to Marbella on Monday for a training camp and face Bournemouth away from home when league action resumes after next week's international break.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
