Matthew Hill's 38th minute goal was enough to give in-form City their sixth successive win.
Danny Wilson's team have taken maximum points from their October fixtures, making him hot favourite for the manager of the month award.
But it was hard going against a determined Huddersfield team, who fought to the last and went agonisingly close to an injury time equaliser.
The decisive goal came when centre-back Hill burst out of defence and exchanged passes with veteran midfielder Brian Tinnion, whose superb return ball created space for the youngster to shoot low past Scott Bevan.
With both teams operating 4-5-1 formations, it proved a game of few clear chances.
Jonathan Stead was a lone striker for Huddersfield while Christian Roberts did the same job for City.
Huddersfield were more adventurous in the second half and had Wilson's men hanging on in an exciting finale.
City goalkeeper Steve Phillips had to produce a fine injury time save low to his right to keep out Danny Schofield's 25-yard shot, which skimmed off a wet surface.
From the resulting corner Bevan moved forward from his goal at the other end to head narrowly wide.
City just about merited victory for having the edge on possession, but created few openings themselves in a match of quality passing but little penetration.
Tinnion had a first-half free-kick well saved by Bevan while Roberts sent a glancing header narrowly wide in the closing stages.
Huddersfield suffered a blow just before the interval when John Thorrington limped off with what appeared to be an ankle injury. He was replaced in midfield by substitute Simon Baldry.
The kick-off was held up for 15 minutes because of traffic and ticketing problems, but eventually a crowed of more than 11,000 witnessed a tense battle