City had 21 attempts on goal plus numerous other attacking opportunities, but only 5 of those 21 were on target.
Lawrie Dudfield came closest when he slid his shot just wide of the post.
The Tigers had a penalty appeal turned down, and Richard Sneekes was booked in the protest. David Beresford's cross from the left was completely missed by Ryan Williams, and the ball bounced up onto the defender's arm. However, referee Mr Cain didn't see it.
That wasn't Williams' only chance, and Gary Alexander, Theo Whitmore and Richard Sneekes among others also had opportunities to find the net.
But it was Huddersfield's Andy Booth who did find goal, 7 minutes before half time. Theo Whitmore foolishly lost possesion in his own half, and Chris Hay's shot from outside the area deflected off Ian Goodison. Paul Musselwhite's reflexes were tested as he got a hand to the shot, but Booth fired in the rebound and now puts the Terriers just one game away from the Grand Final.
City line-up (4-4-2): Musselwhite; Petty, Whittle, Goodison, Holt; Williams, Sneekes (Johnsson), Whitmore, Beresford; Alexander, Dudfield (Greaves).
Un-used subs: Glennon, Mohan, Matthews.