There was a point in this match, with Manchester City losing, when the ball came towards Pep Guardiola and, attempting to control it by the touchline, one of the more cultured footballers of his generation slipped over in his shiny brown shoes, ended up on his backside and got back to his feet with white paint on his overcoat. His team were struggling, the crowd were anxious and City were in danger of a result that would have meant going into Christmas outside the Premier League’s top three for the first time since 2009 – or, to put it another way, just after Mark Hughes had been sacked.

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The turnaround in the second half was considerable and, by the end, it felt as if City may have reminded everyone they are not out of this title race just yet. “We’ll fight to the end,” used to be the soundtrack here under previous managers and, for the first time perhaps, City showed those qualities of endurance under the new regime.

Guardiola could be seen embracing Yaya Touré, a player he had previously ostracised, and City certainly looked better for their new training routine. They had, according to their manager, devoted two and a half hours of every session purely on winning second balls, a tactic that played its part in their first goal of a hugely satisfying victory.

Guardiola has been subjected to so much scrutiny it is only fair to report that his half-time switch was a prominent factor and – well, whaddya know – he does know what he is doing, after all. It was the fluency of City’s attacking, in particular the interchanging of positions between David Silva, Kevin De Bruyne and the two scorers, Leroy Sané and Raheem Sterling, that wore down their opponents. Each member of that quartet had a go as the team’s most advanced central player. Yet City did not have an orthodox striker, preferring to operate with two men in wide positions and another two in the role of elusive No10s.

It was a blur of movement and the two passes to set up the goals – one from Silva, one from De Bruyne – felt like a reminder that winning for Guardiola is not enough. He wants to do it with panache, style and supremacy and he could probably be excused that pithy little aside when he was asked about the tactics he had employed to counter Theo Walcott’s early goal. “Now we’ve won the trainer is a genius, right?” Guardiola said. “A genius.”

In the process, it left Arsenal mulling over back-to-back league defeats for the first time since April 2014, leaving them nine points off Chelsea at the top, with City moving into second position, and Arsène Wenger talking about “a horrible week, absolutely horrible” bearing in mind they had also surrendered a winning position against Everton in their previous match. Wenger was visibly angry with Petr Cech when, in the final seconds of stoppage time, the goalkeeper played a short free-kick rather than aiming it into the opposition penalty area and a distressing afternoon for Arsenal was compounded by Alex Oxlade‑Chamberlain’s hamstring injury, shortly after coming on as a substitute.

Oxlade-Chamberlain could not hide his anguish, throwing his shirt towards the dugout before heading straight down the tunnel, whereas Wenger resorted to blaming the match officials, arguing both goals were offside as well as noting: “Referees are protected very well, like lions in a zoo.” A nice line but it could also be said his own team had a few lions during the second half – if we are talking about the variety from The Wonderful Wizard of Oz, in need of some courage.

Wenger said his team “dropped physically” in the second half and “maybe we dropped a bit mentally” after Sané’s equaliser two minutes after the restart, and these were not hugely encouraging remarks for a team supposedly harbouring realistic title aspirations. Mesut Özil, Alex Iwobi and Walcott caused considerable problems in the first half but they all tailed off. That, in turn, isolated Alexis Sánchez, whose expertise had sent Walcott running into the penalty area for the opening goal.

As for the criticism of City’s goals, if Sané was offside it was by the width of a cigarette paper and an argument could be made either way about whether Silva was obscuring Cech’s vision when Sterling let fly with the left-foot shot that beat Arsenal’s goalkeeper at his near post. Yes, Cech would have been aware of Silva’s presence but he still had a clear sighting of the shot.

Sterling had started the game in the void left by Sergio Agüero but the experiment seldom worked in the first half, most notably when he flashed a header wide from the kind of opportunity City’s suspended striker would take as a matter of routine. After the break, Sterling switched back to his usual right-sided role and, first, it was Sané’s turn to have a go through the middle. The 20-year-old, signed from Schalke for £37m, has taken his time to show why Guardiola made him one of his priority signings but he had a fine second half, showing great composure for the equalising goal and persistently troubling his opponents thereafter.

Arsenal seldom threatened Claudio Bravo’s goal in the last 20 minutes and City duly completed their first win, having been behind at half-time, since November 2012.