The in-form Cherries notched an impressive fifth straight league win as they appear to be heading menacingly towards the play-offs.
Jonathan Woodgate’s side moved up to fifth in the table, five points ahead of seventh-placed Reading.
The Terriers, meanwhile, have now won just once in their last 10 matches and still have work to do to secure their second-tier status.
On a sun-drenched early evening in West Yorkshire, it was the visitors who threatened inside the opening minute.
Arnaut Danjuma touched the ball through for defender Lloyd Kelly, and his poked effort was well saved at the near post by Ryan Schofield.
With so much at stake, and given their impressive recent form, it was no surprise to see the Cherries very much on the front foot early on.
Bournemouth surged ahead in the 15th minute, and it was former Huddersfield favourite Billing who did the business.
The £15million man dived in to head a rebound into the empty net after Danjuma’s low shot was parried by Schofield.
It was no more than Woodgate’s men deserved, but they were almost pegged back soon after when Aaron Rowe forced Asmir Begovic into a smart near-post save.
Just before the half-hour mark the Cherries ought to have stretched their lead.
Adam Smith darted round the back before pulling a cross back for Danjuma, but he blazed wildly over the top from eight yards.
Two minutes before the break the visitors were in again.
Latching onto a long ball forward from Kelly, Dominic Solanke raced clear before dragging a shot wide.
Solanke made no mistake seconds later, however.
He picked up Ben Pearson’s short pass before crashing home sweetly past Schofield from 20 yards.
Four minutes after the restart the woodwork rescued Bournemouth.
Lewis O’Brien ran down the left and, after playing a neat one-two with Rowe, his powerful strike hit the angle of post and bar.
That was undoubtedly a scare for the Cherries, but they remained in control as the hour mark passed at the John Smith’s Stadium.
They continued to press, and skipper Steve Cook was almost an unlikely scorer when his stabbed effort from close range was blocked by veteran Richard Keogh.
A similar strike from Solanke - albeit from a little further out - was bravely blocked by Naby Sarr.
Terriers skipper Jonathan Hogg nodded home Duane Holmes’ corner kick in the 76th minute to give the hosts hope, but they failed to test Begovic again in the closing stages.
Bournemouth substitute Sam Surridge forced Schofield into a fine fingertip save just as the game went into additional time, and the visitors ran out winners.
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