Two first-half goals and a penalty save earned City a vital victory on the road to leapfrog their hosts in torrential rain in West Yorkshire.
Jonathan Kodjia helped in Marlon Pack’s devilish free kick to score goal number nine of his debut season in English football to put the visitors in front inside seven minutes.
But within four minutes City owed a debt of gratitude to goalkeeper Frank Fielding for guessing right – to his left – to deny Huddersfield’s Emyr Huws from the spot.
It was Aden Flint who reacted quickest to clear the loose ball, before the defender showed his effectiveness at the other end to head home Luke Freeman’s free kick.
The home team continued to probe with patient football, but it was the more direct approach from Harry Bunn that handed them a lifeline with six minutes to go, as the substitute finally found a way past Fielding with a thunderous 30-yard drive, but City held on for maximum points.
Steve Cotterill made four changes to his side beaten at home by Blackburn Rovers last time out.
Two of which were enforced, with Nathan Baker and Derrick Williams suspended and injured respectively, meaning a new-look left side with Liam Moore and Joe Bryan filling the void.
Elsewhere, Pack returned from his ban to replace Bobby Reid in midfield, while Aaron Wilbraham was recalled to partner Kodjia up front.
As is often the case, City started brightly. Luke Freeman stung the palms of goalkeeper Jed Steer before Kodjia glanced home Pack’s inswinging free kick with a deft header.
Steve Cotterill’s men finally had the opening goal that has eluded them in recent weeks, but within four minutes Huddersfield were presented with the perfect chance to cancel out City’s lead.
Huws embarked on a positive surge from midfield that carried him deep into visiting territory before slipping the ball to his left for Nahki Wells, who got his body in front of Luke Ayling and duly went to ground when contact arrived from the retreating defender.
Referee Jeremy Simpson wasted no time in pointing to the spot to signal the fourth penalty City have conceded in five matches.
But Fielding duly doubled his tally of spot-kick saves for the season by diving low to his left to keep out Huws’ penalty before the Welshman was bravely kept out on the rebound by the anticipating Flint, who threw himself in the way to preserve City’s clean sheet.
The big defender would have to receive extended treatment whilst his team-mates were forced to stem the flow of Huddersfield attacks a man light.
Town had enjoyed plenty of possession but City still carried a threat going forward. Wilbraham turned well on the edge of the box and forced a save from Steer on his left foot before he was crowded out in attempting to meet Elliott Bennett’s chipped cross.
But it would be another set-piece goal that offered Cotterill’s side some breathing space on 29 minutes.
Again it was a free kick awarded on the City left – slightly more central than the last but still outside shooting territory.
This time Freeman was the provider, drilling a flatter delivery towards the back post where Flint pulled away to score with an excellent header back across Steer’s dive.
Suddenly you could see the confidence coursing through the City players. Korey Smith, typically busy in midfield, spread the ball wide to Bennett, whose low centre ran just beyond the stretching Kodjia and went unconverted by Wilbraham behind him – possibly unsighted by his strike partner’s attempt to score.
Fielding was having to be alert at the other end, not helped by a greasy surface as the rain continued to teem down, with the City number one saving smartly from Joe Lolley and Wells on a couple of occasions including a fierce drive that was creeping inside the near post.
Huddersfield were prepared to take risks and left gaps as a result. Freeman was enjoying himself in midfield and found the advancing Bryan, who crept into the box and went for goal on his right foot with a shot that landed kindly into the path of Kodjia, who could only prod the ball into the arms of Steer.
Bennett was again proving a problem for City’s opponents down the opposite flank and delivered another teasing cross this time met by Moore at the far post, but the defender sent his shot high over the bar from eight yards.
City resumed their efforts to put the game to bed after the interval. Again Freeman combined with Bryan, as this time the Bristolian’s cross was kept out by a combination of the back-pedalling Steer and his crossbar.
But the Terriers were always likely to make a game of it and Ben Chilwell should really have hit the target with a free shot from 12 yards that he dragged fractionally wide.
Fielding adopted an unorthodox approach to deal with another stinging effort from Wells, this time punching the wet ball back into play where Sean Scannell could only fire high and wide on the stretch.
Then Lolley stepped inside and drilled a low shot that for once had Fielding beaten but clipped the keeper’s right-hand post on its way wide.
Huddersfield’s commitment to playing out from the back nearly backfired when Steer gave the ball straight to Freeman 35 yards from goal, the midfielder rushed the chance and sent his first-time lob sailing over the top.
Just when it looked like the hosts might have run out of ideas, Bunn chanced his arm from distance to score with a bolt from the blue, before Fielding made a priceless stop from another replacement, Kyle Dempsey, as Town’s late pursuit of a share of the spoils proved in vain.