Goals from Danilo, Raheem Sterling and Leroy Sane had the Blues in cruise control before the hour-mark.
The champions settled for the 3-0 win and a fourth successive clean sheet in what has so far been a stunning start to the New Year.
City began at a measured pace, perhaps gauging how the managerless hosts would approach the opening minutes.
The Blues enjoyed the majority of possession without threatening the Terriers’ goal too much to begin with, but just 13 minutes in and City fans were left scratching their heads as Sterling was felled in the box by Rodney Kongolo.
It looked a clear penalty. But – as we’ve seen a number of times this season – the officials saw no foul.
Fortunately, the champions didn’t have too long to wait to open the scoring.
Just five minutes later, Danilo fired in a shot from distance that Christopher Schindler stooped in the way of and glanced past his own keeper.
Danilo’s effort brought up a century of goals for City this season and meant we were the fastest side to reach the notable milestone in Europe this term.
The Blues were certainly not at their fluid best and the Terriers were snapping into tackles and defending in numbers.
But it was enough to go into the break with a slender advantage.
City came out refocused and re-energised for the second half and within 11 minutes, had put the game to bed.
The passing and tempo was much better and the second goal of the afternoon came on 54 minutes as Sane narrowly avoided the assistant referee’s flag before delivering the perfect cross for Sterling to send a diving header into the net.
Two minutes later, the lead was three – and what a goal it was.
As the ball came to Danilo just inside the halfway line, there seemed little threat to the hosts – but the Brazil defender pinged a ball to Aguero whose cushioned reverse header allowed Sane to burst into the box and coolly slot home under the keeper.
City could have had another when Bernardo raced into the box, but his shot was saved and the champions declared at three as the nip and tuck nature of this season's title race continues.
What it means…
City move back to within four points of leaders Liverpool while again improving our goal difference.
The Blues will play first in the next round of fixtures with the away fixture at Newcastle coming 24 hours before Liverpool’s home clash with Leicester – a chance to narrow the gap to one points – albeit briefly.
Star man: Leroy Sane
An assist and a goal for City’s German winger who was inspired form all afternoon.
"The way we played we didn't deserve more than three goals. We will improve in the future. We have to demand more from ourselves in every game and do our best, but sometimes it's difficult. They defended deep and man to man
“In the second half we were better, especially the first 15. Our rhythm was not quick enough in the first, but we would take that result.
“I am honest with them and tell them all the time what I feel.
“We have to try and find the reason why we didn’t play quicker or better.
“After what these guys have done in 16, 17 months, it can't be lack of intensity or not wanting to run.
“We didn't make passes in a row, we had to move it quicker. We spoke about what we should do in the second half.
“We have to demand from ourselves to do our best every game. So far, we have been incredible. Champions League, one step from Carabao Cup final.
“We have incredible points - 56. It’s a lot of points. But every game teaches us and shows us what we have to.”
The Blues return to domestic cup again this week.
With a 9-0 aggregate going into to Wednesday’s Carabao Cup semi-final, second leg, City should confirm a place at Wembley at the Pirelli Stadium against Burton Albion.
And the Blues can take a step towards the FA Cup last 16 with victory over Sean Dyche’s improving Burnley next Saturday at the Etihad Stadium.