Alex Pritchard fired Huddersfield in front after seven minutes and although Junior Stanislas levelled, the hosts were ahead again before the break thanks to Steve Mounie's 27th-minute header from Aaron Mooy's delivery.
A late penalty from Rajiv van la Parra put the icing on a big victory for the Terriers after Pritchard was brought down in the box.
Mooy had his head in his hands as he was taken off but fears of a serious injury for the Australia midfielder ahead of the World Cup in Russian Federation have been allayed, with British broadcaster BT Sport saying it was a deep cut.
"We had hard fixtures behind us and now start games when we can be competitive", said Wagner, whose team are now just four points behind the 10th-placed Cherries.
Trump Will Not Immediately Release Democratic Memo, Suggests Revisions
We know that was his motive because he told us so, bragging that with the memo's release, he had somehow been vindicated. Schiff's comments come after the White House's decision last week not to publish the Democratic rebuttal document.
The clash between Premier League sides Huddersfield and Bournemouth was well into the dying stages when the cameras panned to Huddersfield manager, David Wagner, watching on from the sidelines.
Steve Cook then scored an own goal from Mounie's deflected shot with just under 25 minutes to play.
"It was our idea to press the opponent high up the pitch and win the ball. Every game should be treated as a cup final", said Howe.
Bournemouth are the seventh team Huddersfield have beaten in all four tiers of English league football, along with Bradford, Brentford, Bury, Grimsby, Portsmouth and Watford.