Manchester City reeled off a 10th win in 11 unbeaten games across all competitions and Erling Haaland returned from a foot problem to enjoy a 20-minute cameo. The champions’ pursuit of a historic fourth consecutive crown is rolling along nicely, this victory decorated by two goals from Julián Álvarez on his 24th birthday.

That took his tally to 15 and the man for whom he has been deputising in attack, in a first involvement after 10 games, had the chance to add his 20th of the term and make this a perfect comeback. But, totally against type, an embarrassing Haaland miskick ensued after he took aim.

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He and Pep Guardiola did not care, however, because victory and maintaining the pressure on Liverpool was the task, which City did with ease. They remain five points behind Jürgen Klopp’s side with a game in hand and have the same 46-point total as Arsenal.

Guardiola said: “We know that if we drop points with the quality that Arsenal and Liverpool have [it will be a problem]. I know how strong they are but still we are there. It’s not just three – Tottenham and Aston Villa are still there [on 43 points].”

A two-goal burst inside the half-hour effectively killed this contest. After a blocked Matheus Nunes shot the same player created City’s opener. Taking a return from Phil Foden, the Portugal international skipped down the right with his nearest colleague Josko Gvardiol, who had run into the area from left-back. But Nunes spied Álvarez in a plum, close-range heading zone, dropped the ball into him, and the striker could not miss.

This had Vincent Kompany trudging back to the bench, cursing how easy it was for City. Moments later, Jérémy Doku was given the freedom to jink and cross: James ­Trafford spilled the ball and yet Burnley escaped.

Not for long. A classic Kevin De Bruyne surge through midfield drew a foul. Thinking quickly, the Belgian curved the free-kick along the grass to the left of the wall and Álvarez, bending a run, swished his right boot through the ball and beat Trafford to the goalkeeper’s right. This was Premier League assist No 104 for De Bruyne, pulling him ahead of Wayne Rooney on the all-time list.

A 2-0 lead after 22 minutes suggested City’s 21st league game this season might already be over. Yet when Wilson Odobert slipped in Lyle Foster, a Gvardiol sliding challenge was required to thwart the centre-forward. Guardiola, fresh from congratulating a City coach – presumably for the free-kick move – became martinet, demanding his players wake up.

They did. Gvardiol, applying a silken touch, threaded in Foden who went close to unloading a shot, as Burnley – who had arrived second from bottom and with no win in four games – continued to show why. Nunes, impressive in a roving role, popped up on the left and flicked the ball towards goal as once more the visitors diced with disaster. They were so lax that City could take turns to load up and take a shy at Trafford’s goal: Gvardiol did and narrowly missed when connecting on a diagonal pass from the left.

Foster ended the half with a dip of the shoulder and an effort that flew past Ederson’s left post. It was, at least, a glimmer of encouragement for Burnley.

This emotion was killed off by what occurred 27 seconds into the second half. Foden trotted along the right and passed to Rodri who calmly found Trafford’s bottom-left corner.

Last March City hammered Kompany’s side 6-0 in an FA Cup tie and the spectre of a similar scoreline was raised. Zeki Amdouni spurned a chance to at least chalk up a consolation when sprinting forward by spraying the ball over Ederson’s bar.

To further demoralise Burnley, Haaland began warming up, drawing a rousing cheer from the home faithful. The Norwegian stayed out, watching City tap possession about as they do so slickly.

When the striker returned to his seat the contest had flatlined. City’s only threat was complacency and so Guardiola called for Haaland, who last laced his boots up for the 1-0 loss at Aston Villa on 6 December.

The next goalmouth action was at the other end, though. Connor Roberts felled John Stones – featuring again after a month out – and an unhappy Rico Lewis squared up to him. The heft of Ederson intervened, City’s No 1 and Roberts being booked. In added time, Ameen al-Dakhil grabbed a consolation for Burnley.

“It’s never great when you lose,” Kompany said. “We have to move on against Fulham [on Saturday].”