Nahki Wells had put the Terriers ahead before Tom Lawrence grabbed an equaliser but Adam Clayton lashed in a late winner for the visitors to leave the Glovers six points from safety and rooted to the bottom of the table with two matches remaining.
Yeovil now require an improbable set of results and a considerable swing in goal difference to maintain their second-tier status.
The hosts came close to notching an opener inside three minutes when James Hayter headed Kevin Dawson's drilled cross over the bar.
Huddersfield, who made the 250-mile trip south without a win in their last 10 league matches, started slowly and should have conceded moments later when Hayter's header beat Alex Smithies but rattled the crossbar.
The visitors awoke from their slumber soon after when Oliver Norwood teed up Adam Hammill, but his tame effort trickled into the arms of goalkeeper Marek Stech to sum up a half in which both sides lacked conviction and composure in the final third.
Welsh winger Lawrence looked the most likely to break the deadlock for the Glovers and he forced Smithies into a good save when his fizzing free-kick appeared to be spiralling towards the top corner.
Moments later the 20-year-old spurned a glorious opportunity as he galloped through on goal following a defensive mix-up between Anthony Gerrard and Murray Wallace. However, his decision to try and take the ball around Smithies backfired as the giant stopper got down quickly and plucked the ball from the youngster's feet.
Following an injury to winger Danny Ward early in the second half, Huddersfield substitute Sean Scannell almost made an instant impact. Twisting and turning away from Byron Webster, he laid the ball back to Jonathan Hogg at the edge of the box but the midfielder drilled his shot wide of the target.
Yeovil, who themselves came into the match short of form with only one win in their last 10 matches, continued to labour in front of goal and were left cursing referee Stuart Attwell shortly before the hour mark when Lawrence appeared to be tripped inside the box, but his claims were waved away.
The visitors snatched the lead following a swift 69th-minute counter attack when Hammill darted down the right flank from inside his own half before superbly guiding the ball to the back post for Wells to bundle home from close range.
But three minutes later Yeovil's survival hopes were resurrected when Lawrence's fierce free-kick dissected the Huddersfield wall and flew past Smithies.
Gary Johnson's side pushed for a late winner in eight minutes of added time following Ward's lengthy treatment, but midfielder Clayton stunned Huish Park by drilling a late decider with seconds remaining to leave Yeovil's relegation to League One all but mathematically confirmed.