City gave away a second goal following another defensive blunder four minutes before half time. Andy Dawson - under pressure from Stead on the byline - passed the ball to Richard Hinds to clear. But the right-back slipped over, and Stead passed the ball across goal to Andy Booth who smashed it home.
A minute before the break, Jason Price retaliated to a late challenge from Tony Carss, and both players were shown yellow cards.
City came out in the second half looking to take the game to Huddersfield. Danny Allsopp was clean through on goal but Paul Scott made a last gasp clearance before he could shoot, and Stuart Elliott had a volley deflected wide.
Joseph gave away a free kick in a dangerous position, but Carss was just off target. Booth and Worthington were also denied, while Stead headed wide.
Jamie Forrester and Ryan France both came off the bench, but the Terriers added a third following yet another mistake. Joseph missed the ball, and as he attempted to tackle back he played the ball into the box to Danny Schofield. No defender could get a block in as he thumped the ball past Fettis for 3-0.
City replied with a fierce shot from Stuart Green that was tipped over by the fingertips of Phil Senior, and Jamie Forrester got a last minute consolation goal to pull it back to 3-1, but the late efforts weren't enough to make up for the atrocious defensive howlers that gifted Huddersfield the win. City were booed off by the 3,884 travelling fans, while the 10,007 home fans were ecstatic with a win following a string of four defeats.
City line-up (4-4-2): Fettis; Hinds, Joseph, Delaney, Dawson; Price, Green, Ashbee, Elliott (France 78); Allsopp (Forrester 64), Burgess.
Un-used subs: Musselwhite, Whittle, Holt.