Forward Junior Stanislas briefly put Bournemouth level but the Cherries succumbed to a first defeat in eight top-flight matches.
Huddersfield's only victory in their last 11 games against Bournemouth was by 5-1 in the Championship in August 2013.
Aaron Mooy was the provider for Mounie's goals - a header from a free kick in the 27th minute and a steered finish in the 66th - but his game ended early when he was carried off the field on a stretcher with a left knee injury.More news: JB Hi-Fi shares slump on margin warning
The Socceroos star played a decisive role for the Terriers as they secured a key victory in their battle against relegation, laying on two assists for Steve Mounie in their 4-1 win over Eddie Howe's side.
Wagner was directly asked about potential ligament damage for the Aussie, which he confirmed is not the case.
Huddersfield's Jonathan Hogg is challenged by Bournemouth's Lewis Cook.More news: Jose Mourinho digs out Alexis Sanchez & Anthony Martial after Manchester United defeat
Huddersfield continued to look the more threatening at the start of the second half, with Pritchard firing into the side netting and Mooy dragging a 20-yard effort narrowly wide of the bottom-right corner. It was a fine goal. Huddersfield might have been expected to wilt first, given the energy expended, but on 67 minutes Pritchard led from the front again, closing down Nathan Ake. Instead Van la Parra took responsibility to stroke home.
Another cross, this one met by Mounie, who, via Cook, scored the third and in six minutes of added time, Van La Parra added a fourth from the spot after Dan Gosling and Ake had upended Pritchard.More news: Amid Olympic Détente, Pence Snubs North Koreans In Visit To Pyeongchang
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