It is not a stretch to say Manchester City barely moved out of second gear and were still a class above Bournemouth. This was a record-extending 17th consecutive Premier League win and with Newcastle United, Crystal Palace and Watford to complete their festive programme, by 2 January the run may be 20.

This would beat the 19 on the spin Guardiola recorded with Bayern Munich and, despite sport’s unpredictability, you do start to wonder how City will be stopped.

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When Sergio Agüero headed Bernardo Silva’s cross home on 79 minutes for his second it completed 100 City Premier League goals in the competition for the calendar year and had the home faithful singing: “We’ve got Guardiola,” an apt tribute to a manager whose magic is imbued throughout this side. Ever the arch-perfectionist, the 46-year-old believes City can improve.

“Attack more fluently, more chances, it is not easy when the opponents stay back,” Guardiola said of Bournemouth, who defended with five. “We have to learn to improve and attack this kind of defence and I think that is going to happen – our target is what we do to find a solution.”

The hunt to extend the victorious sequence began with an XI showing two changes, Vincent Kompany and David Silva coming in for Eliaquim Mangala and Ilkay Gündogan. Bournemouth brought in Callum Wilson, Dan Gosling, Junior Stanislas, Steve Cook and Jack Simpson, the last of these making his Premier League debut.

Almost immediately, City found their rhythm. Kevin De Bruyne and Kyle Walker combined before the former swept in a ball that required Cook to stoop and head away. After 11 minutes the Cherries were disrupted when Stanislas appeared to suffer a leg injury and was replaced by Marc Pugh.

So supreme have City been that the expectation is of a near-domination of the ball and a medley of chances. Yet while the first part proved true, the second did not occur for a while due to a surprising lack of quality in the final pass.

In a flash, though, this changed. Nicolás Otamendi strode upfield, flipped the ball beyond Bournemouth , and in a single movement Agüero controlled and hit a shot over the advancing Asmir Begovic – it was too high but a sure sign City were livening up.

Next, Leroy Sané claimed a corner along the left. David Silva delivered and Fernandinho headed over. Later, came a collector’s item: a long-distance shot from a City player – Otamendi striking the ball truly and causing Begovic to fling himself to his right.

Now, finally, City scored. Against this Guardiola team the last thing needed is an unforced error. Yet this is what occurred when Begovic fluffed a regulation clearance. Fernandinho beat a dawdling Jordon Ibe to the loose ball and clipped possession to David Silva.

Back came the ball and the Brazilian’s superb left-footed cross found Agüero, who half-kneeled to head past the hapless goalkeeper. It was his 14th goal in 20 games and the 100th of a glittering City career at this venue.

For the rest of the first half City coasted. But at the break Guardiola’s instruction to his players may have sounded terse: be more ruthless.

If a listless start did not augur well then what happened on 52 minutes reversed that notion. This was a classic Guardiola move as David Silva used De Bruyne’s run as a decoy, rolling the ball instead to Agüero. The No10’s instant sand-wedge of a chip found Raheem Sterling and he smashed in for his 16th goal of a standout campaign.

From here the contest flatlined for a time. Guardiola took off Sané and De Bruyne for Bernardo Silva and Gündogan and now City doubled the scoreline. First came Agüero’s header, then came Danilo’s debut goal, the substitute hammering home from Sterling’s pass.

Eddie Howe’s side will spend Christmas Day in the relegation zone. “We’ve had an incredibly difficult run but we are through it and have to focus on the games coming up,” he said. “Every game is important, but the next three take on huge importance for us. We have so many injuries and it’s not ideal at this time of year. We try to approach every game looking to win. But they are a difficult team to play against, if you get it wrong here they have the players to expose it.

“We came with a game plan to stay in the game then maybe have a go. For long periods we were good, the [opening] goal came from our mistake which was disappointing but the rest of the half was OK.”

Despite City’s aura of invincibility Howe believes they can be downed. “Anyone is beatable, you can’t tell what will happen. We had moments when we could have scored and it could have been different.”

Yet this Guardiola team is making the sport seem so simple.