Danilo's deflected long-range effort brought up that landmark, achieved across all competitions, after 18 minutes but Pep Guardiola's side were some way from their fluent best during the first half.
Raheem Sterling headed home the crucial second early in the 54th minute before fellow winger Leroy Sane got in on the act, puncturing a buoyant Huddersfield crowd that came to celebrate David Wagner's tenure.
Caretaker boss Mark Hudson stepped in after Wagner's departure this week and oversaw a battling display, albeit from a team 10 points from safety at the foot of the table.
Sergio Aguero prodded wide in the third minute after exchanging passes with Sterling, whose strong penalty claims fell on deaf ears when he was brought down by Terence Kongolo.
City were unlucky on that occasion, but their opening goal came with a slice of fortune as Danilo's speculative drive spun off Christopher Schindler and beyond the helpless Jonas Lossl.
Ilkay Gundogan went close to doubling the visitors' lead as the end of a scrappy opening 45 minutes approached.
The Germany midfielder was involved in the move that put the game beyond Huddersfield as Sane stayed just onside to collect Kevin De Bruyne's pass for Sterling to head home.
Sane went from provider to scorer two minutes later as he darted on to Aguero's clever knock down and dispatched a bouncing ball past Lossl.
City substitute Bernardo Silva was denied by Lossl before lively Huddersfield replacement Steve Mounie blazed his side's best chance wide in the final action of the contest.
City have appetite for the chase
Since back-to-back defeats against Leicester City and Crystal Palace handed Liverpool the title initiative last month, Guardiola's men have won six consecutive games in all competitions, scoring 22 unanswered goals in their past four. That untimely wobble is receding from view and, with the likes of Aguero, De Bruyne and David Silva all working back towards full match sharpness, there should be more to come.
Sterling relishes a hostile battle
Andre Marriner's decision not to award Manchester City's right winger a penalty early on truly beggared belief. Sterling had already been bizarrely singled out for boos by a section of the home faithful, but he seems to revel in making a mockery of such nonsense nowadays. Having scored a late winner at the John Smith's Stadium last season, the England star again produced the game-breaking contribution.
Lowe fails to keep the high line
It seems harsh to single out any of Huddersfield's tireless defensive unit after their efforts ended without reward. However, it must have been galling for the collective to see Chris Lowe's concentration waver and play Sane fractionally onside for Sterling's goal. It was a yard of space the Town left-back could scarcely afford to give to his countryman.
