Huddersfield TOWN remain 10 points adrift of safety at the foot of the table after a ninth defeat in their last 10 league matches.
The result saw Manchester City keep the pressure on Premier League leaders Liverpool with a routine win over managerless Town.
But it was a sobering end to an emotional week for the West Yorkshire club following the departure of head coach David Wagner, although caretaker-boss Mark Hudson can be proud his players gave him their all.
Danilo’s deflected effort gave City a half-time lead before Raheem Sterling and Leroy Sane both struck in the space of two minutes early in the second period.
A fourth straight league win since their Boxing Day defeat at Leicester City has lifted manager Pep Guardiola’s side back to within four points of Liverpool in pursuit of back-to-back titles.
Hudson, meanwhile, was clearly intent on stamping his mark on Huddersfield by making six changes.
But they had barely settled when Sergio Aguero, back in City’s starting XI after a three-game absence, spurned an early chance as his side enjoyed plenty of immediate possession.
Huddersfield also created an early opening, but Adama Diakhaby, making just his third Premier League start, misdirected his header from Elias Kachunga’s cross.
Sterling was furious when referee Andre Marriner waved away his appeals for a penalty after he had clearly been fouled by Terence Kongolo.
But City took what seemed an inevitable lead after 18 minutes with their 100th goal of the season in all competitions. Danilo’s speculative drive from 25 yards struck Christopher Schindler’s head and wrong-footed goalkeeper Jonas Lossl.
City were given a let-off in the 27th minute when Kyle Walker escaped with a yellow card for his reckless challenge on Chris Lowe as Town dug in.
The visitors failed to carve out a further chance until Ilkay Gundogan fired wide after good work from Kevin De Bruyne and Walker.
Town fans fell silent during the interval as they hung on every word of Wagner’s farewell message played on the big screen.
But City took little notice and cruised through the gears to add two more goals in the space of two minutes.
Sterling dived to head home Sane’s cross in the 54th minute and the latter stole clear on to Aguero’s lay-off to shoot home from eight yards and seal all three points.
Terriers’ substitute Steve Mounie lifted the home fans with a long-range curling effort that flew narrowly wide and then forced Ederson into a flying save with a header from fellow substitute Alex Pritchard’s cross.
Town were outclassed by a City side that rarely shifted into fourth gear, but avoided the pasting many of their fans had feared.
They would even have scored just their sixth home goal this season had Mounie not miskicked from close range after the ball deflected to him in the box in the final seconds. His miss summed up Town’s season.
Guardiola admitted to disappointment overall with City’s display.
Asked how he could expect his side to get better, Guardiola responded: “Our pace, more passes in a row – we were not able to make a lot of passes.
“Always in football when you play good you have the ball as much as possible.”
Although Danilo’s heavily deflected strike gave City a relatively early lead it was not until Sterling and Sane struck in quick succession early in the second half that the points were made safe by the champions.
Sane revealed Guardiola had demanded an increase in intensity during the interval.
The German winger said: “The second half everyone could definitely see we were quicker and better and in important positions and controlled the game. It is easier when you can play like that and you can push forward more.
“The boss said at half-time that we can’t play the way we were playing and that we had to get better.
“They were putting us under some pressure too and we know in the Premier League that a goal can come out of nowhere and at 1-1 it would be difficult to get the win. So he woke us up a bit to play our game quicker and better and help us find where the space is.”
Huddersfield Town: Lossl, Smith, Schindler, Kongolo, Lowe, Kachunga, Puncheon, Hogg, Bacuna (Pritchard 64), Mbenza, Diakhaby (Mounie 59). Unused substitutes: Hamer, Depoitre, Jorgensen, Hadergjonaj, Durm.
Manchester City: Ederson, Walker, Otamendi, Laporte, Danilo, De Bruyne, Fernandinho (Silva 59), Gundogan (Delph 80), Sterling, Aguero, Sane (Bernardo Silva 72). Unused substitutes: Stones, Gabriel Jesus, Foden, Muric.
Referee: Andre Marriner (West Midlands).