To the credit of Manchester City there are not many other teams who could come up with this kind of feat of escapology from a position at half-time where they were not only losing to one of the Premier League’s coming teams but also playing with 10 men because of the sending off that had spoiled Kyle Walker’s first night in front of his new fans.

By the end, there was even the sense that Pep Guardiola’s players were disappointed they could not complete the recovery and conjure a late, decisive winner once Raheem Sterling, one of their second-half substitutes, had volleyed in an 82nd-minute equaliser.

Morgan Schneiderlin’s late dismissal, after two bookings of his own, had levelled the numbers and City were still smouldering with a sense of injustice at the end because of the nature of Walker’s second booking and the amateur dramatics from Dominic Calvert-Lewin that made it an ignominious home debut for the £50m man.

The game was not short of talking points and Everton ought to be disappointed they could not make it a second successive win given the story of the first half and another goal for Wayne Rooney to advance the theory that he might yet return to the England set-up.

Gareth Southgate, the national team manager, was here in readiness for Thursday’s squad announcement for the World Cup qualifiers against Malta and Slovakia and it is not too outlandish to think Rooney could add to his 119 caps.

This was also his 200th top-division goal, making him only the second player after Alan Shearer to reach that number in the Premier League era, and there was another impressive statistic that showed, approaching the age of 32, he covered more ground than any other Everton player. Calvert-Lewin cannot have been too far behind and it is just a pity, perhaps, that the 20-year-old tarnished an otherwise impressive night with the incident that led to Walker’s second booking in the space of two minutes at the end of the first half.

Walker cannot have too many complaints about the first yellow card for a challenge on Leighton Baines. He was, however, entitled to be aggrieved in the extreme about what happened as he and Calvert-Lewin waited for a high ball to come down. Walker did give his opponent a nudge but it was little more than a gentle reminder of his presence. The collapse from Calvert-Lewin was a deception and the referee, , Bobby Madley, fell for it, having taken the advice of the fourth official, Michael Oliver.

As the players returned to the pitch for the second half, Guardiola was in the tunnel demonstrating to Oliver what had happened with a little nudge of his own and struggling perhaps to conceal the fact he was obviously livid. It is not often the City manager turns on officials in full view of the TV cameras. On this occasion, however, he had legitimate complaints even if Ronald Koeman argued that Schneiderlin might also have been harshly treated for his two bookings, both for fouls on Sergio Agüero.

After being reduced to 10 men, City deserve a lot of credit for still having the ability to trouble the team with the numerical advantage. Gabriel Jesus was removed at half-time and Sterling quickly set about trying to make a favourable impression on the right. Everton were guilty at times of not taking enough care of the ball – Koeman complained that his side had gone long too often – and chose to operate on the counter-attack when the evidence of the first half indicated that Ederson, City’s new goalkeeper, should be put under more sustained pressure.

Ederson was brought in from Benfica, at £34.7m, following a wretched first season for Claudio Bravo and Guardiola could probably be forgiven for thinking the new man should have saved Rooney’s shot. Instead, a rare left-foot effort from the Everton man went through Ederson’s legs, ricocheted off a post and the former England captain was wheeling away to celebrate, cupping his ears to the fans who had been berating him because of his Manchester United connections.

Rooney’s goal was also an ordeal for Leroy Sané given it was his mistake, trying to keep the ball in play, that gave away possession and left City vulnerable to the attack that saw Calvert-Lewin link up with Mason Holgate before laying on the decisive cross.

A couple of minutes earlier, David Silva had cracked a shot against a post and at that stage, it had looked as though City were getting on top. Yet Phil Jagielka in particular was a difficult opponent for Agüero, denying the striker on a number of occasions with some outstanding defending.

Gylfi Sigurdsson, Everton’s record signing, came on for his debut after an hour but City kept pressing and never looked disheartened. Danilo, one of their own substitutes, forced a splendid save from Jordan Pickford and, finally, the home side’s perseverance paid off. Danilo sent over the cross from the right, Holgate’s attempted clearance went straight to Sterling and it was a lovely, instinctive volley he sent flying into the corner of the net.