West Brom have won just once in 14 Premier League games under Alan Pardew and remain seven points adrift of safety, while Huddersfield move up three places to 14th.
The Terriers went ahead early in the second half through Rajiv van la Parra, and doubled the lead when Steve Mounie struck before the hour.
Craig Dawson headed in a Chris Brunt corner to halve the deficit and went close at another set-piece late on.
After winning the first two games of the season under Tony Pulis, the Baggies have won just once in 26 league outings.
Wagner’s side were without the injured Aaron Mooy, but even shorn of the Australian’s energy and creativity they proved to be a handful for their hosts after weathering the early storm.
Pritchard, signed from Norwich in January, made a crucial contribution when his deft touch wrong-footed the defence and gave Mounie the chance to curl the ball around Ben Foster.
They continued to attack even after Dawson’s goal, with striker Laurent Depoitre replacing the impressive Alex Pritchard when a defensive substitution may have been expected.
Following next Saturday’s trip to Wembley to face Tottenham, the Terriers’ next three league matches are against sides currently below them in the table, reviving expectations that Huddersfield might make it to a second season in the elite.
What the managers said
West Brom manager Alan Pardew: “I think it is three wins in 37 games. It is a problem, we just have to find a way to win a game, however ugly it is. It was certainly ugly today.
“I was disappointed with the performance. We worked hard this week and looked good going into the game but it wasn’t reflected in the game.
“Huddersfield knock you out of any rhythm with the way they play and it was a bitty game. We didn’t really have any passages of play. We have two or three flair players missing but we should have had enough to beat Huddersfield really.”
Huddersfield manager David Wagner: “We said this before, it wasn’t a six-pointer but it was a massive game for us and the players showed everything – fighting spirit and attitude.
“It was a final for both teams, we won it and of course I am delighted and happy for the supporters, the players and staff.
“We expected they would be on the front foot. We overcame the first 10 minutes without us conceding a goal. After that it was open, we scored two wonderful goals and kept them as far as possible from our goal.”
Terriers do the double – the stats you may have missed
- Huddersfield Town have won back-to-back Premier League games for the first time since their opening two fixtures of the season.
- West Bromwich Albion are the first side the Terriers have done a Premier League double over since reaching the competition.
- Under Alan Pardew, West Brom have accrued just eight points in 14 Premier League matches (W1 D5 L8), four fewer than their first 14 games of the campaign before his arrival (W2 D6 L6).
- Rajiv van La Parra has scored two of his three Premier League goals against the Baggies.
- Steve Mounie, who has been directly involved in four goals in his last four appearances in all competitions (three goals, one assist), has now scored six Premier League goals for Huddersfield, making him their outright top scorer in the competition ahead of Laurent Depoitre (five goals).
- Five of the West Brom’s last six Premier League goals have been scored via corners, with Chris Brunt assisting four of those.
- In fact, since his Premier League debut in August 2008, Chris Brunt has provided 32 assists from set plays, more than any other player.
- Since the 2014-15 campaign, Craig Dawson has scored 12 Premier League goals; no other defender has more in that time.