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.
Rajiv van La Parra converted a stoppage-time penalty, awarded for Dan Gosling's foul on Pritchard, to take Huddersfield out of the bottom three.
In the Netherlands, Brad Jones continued in goal for Feyenoord but was on the end of a 3-1 defeat against Vitesse Arnhem.
Victory did come at a cost for Huddersfield with Australian midfielder Mooy leaving the pitch on a stretcher in the second half after a clash of knees.
Iranian scholar and environmental activist dies in prison
His son Raam Seyed Emami, a popular Iranian singer, tweeted on Saturday: 'The news of my father's passing is impossible to fathom. The singer said that his father was arrested on January 24 and his mother Maryam was informed of the death on Friday.
Mounie has struggled for consistency since becoming the Terriers' record signing at £11.5million in pre-season, but he produced arguably his most complete display in England, impressively leading the line to inspire the side's first league win since 16 December. "He got a cut over his knee - he got some stitches as well", Hudderfield manager David Wagner said.
"We have to see what he looks like in the upcoming days - how long he will be sidelined. It was a fantastic afternoon for us".
Manchester United will play their first game with video assistant referee technology against Huddersfield Town in the FA Cup fifth round this month.
Bournemouth become the seventh team that Huddersfield have beaten in all four tiers of English league football.