Danilo’s deflected shot gave City the lead in an opening half in which they were not at their sharpest.
That goal took City’s goal tally to 100 in all competitions this season — making them the only club in Europe’s top five leagues to reach that total.
Pep Guardiola’s side upped the tempo early in the second half and Raheem Sterling headed in their second goal in the 54th minute before Leroy Sane made it 3-0 two minutes later.
It was a poor advert for the Premier League with Huddersfield, who look almost certain to get relegated and who parted company with manager David Wagner this week, offering next to nothing as an attacking force.
City’s fourth consecutive win since back-to-back losses over Christmas took them to 56 points from 23 games with Liverpool on 60 after they beat Crystal Palace on Saturday 4-3.
Toothless Huddersfield, who had caretaker boss Mark Hudson in charge for the first time, have only 11 points and are 10 points behind Newcastle United who are 17th.
City had scored 19 goals in their previous three games without reply — including two Cup romps against lower league opponents — but they were subdued in Sunday’s first half.
“The way we played we didn’t deserve more than three goals,” Guardiola said. “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.”
Huddersfield set out their stall from the start, retreating back behind the ball to try to frustrate City.
It worked but City did get ahead in the 18th minute when Danilo let fly from range and the ball flew off the head of defender Christopher Schindler past keeper Jonas Lossl.
Despite their clear superiority, City did not add to their total before halftime and it was not until after the break that they rediscovered the slick passing for which they are known.
An intricate spell of passing ended with the ball being played to Sane inside the area and his cross was met with a diving header from Sterling.
Two minutes later Danilo intercepted a wayward pass and his first-time ball forward was cushioned by the head of Sergio Aguero to Sane who neatly side-footed inside the post.
“This game can teach us and show what we have to do to improve,” Guardiola said. “We’ve scored a lot of goals. So far, so good. One team has been better but we’re in January and there’s many more games to play.
“You don’t win or lose the Premier League in January. We have to focus on what we have to do. If Liverpool win, we have to win. And if Liverpool lose then we also have to win.”