Manchester City end the festive period with nine points from their four games after two Gabriel Jesus strikes handed Carlo Ancelotti a first defeat in charge of Everton via a characteristically relentless display.

Pep Guardiola said: “We played top, I am so delighted about the performance. Teams who have been champions and are far away from the leaders can give up and finish seventh or eighth. Maybe we will but not because we don’t try.”

City’s sole reverse of the Christmas programme came last Friday at Wolves in a result that, surely, killed any hopes of catching Liverpool. Instead, their FA Cup defence begins on Saturday, with the Carabao Cup semi-final first leg against Manchester United on Tuesday, then in February the restart of the Champions League; all competitions on which City can now focus intently.

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The notable name in the home lineup was Claudio Bravo, the hardly reliable goalkeeper playing a second successive time because of Ederson being ill following a one-match suspension. The last time Bravo faced Everton – in January 2017 – he allowed four goals from four shots and he added to the count here by being culpable for Richarlison’s consolation.

Ancelotti initially made the same number of changes as his opposite number before Bernard suffered a cut leg in the warm-up, so Tom Davies was drafted in for the Brazilian.

The opening period proved low grade. An error from Ilkay Gündogan had Guardiola muttering and Davies pouncing as Everton transformed defence into an attack that ended with Gylfi Sigurdsson flipping the ball to Séamus Coleman: his effort was tipped behind for a corner by Bravo.

When Gündogan later tried his own chip into Riyad Mahrez, Jordan Pickford was less sure: he dropped the ball and Everton were relieved to clear.

João Cancelo has struggled for form since joining City yet he appeared to have created an opener for Phil Foden only for VAR to rule Mahrez offside. Ancelotti had a consoling word for Guardiola who smiled and later agreed with the decision. “I think it was offside,” said the Catalan.

VAR’s next involvement was confused as it checked for a possible penalty despite Mahrez seeming to be flagged for offside or handball or both. The spot-kick was not given but the contest had been disrupted and, inevitably, the invective-filled anti‑VAR chants had a second airing.

At this juncture both benches were unhappy regarding their respective players’ output. For Guardiola it was Kevin De Bruyne and Foden momentarily losing their deft touch; for Ancelotti it was his men’s sluggish pace and an insistence on passing back to Pickford, instead of looking forward and for the positive.

Better from City was a Mahrez swivel and shot, then a Gündogan effort which also warmed Pickford’s fingers. Really, though, the entertainment level was down, in a sign perhaps of the Christmas and New Year slog. Another was found in the number of offsides committed by tired players – Mahrez a particular perpetrator.

Still, City had dominated the ball and when they do they often prosper. Foden had a snap-shot, gathered by Pickford, and as the break neared Mahrez had two clearer chances but steered the first wide and seemed surprised to receive the second.

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The average fare continued after the interval. Benjamin Mendy sold De Bruyne short so he had to stick a boot out and watch the ball sail into no-man’s land, much to Guardiola’s chagrin. Next Bravo punted possession straight out when Cancelo was the target.

Then, though, came a moment to remember. Gündogan slipped a pinpoint pass into Jesus, who in an instant had beaten Pickford with a finish that was the Brazilian’s 13th goal this season.

From the restart Everton claimed a corner – to Guardiola’s annoyance – but despite a second one following when Dominic Calvert-Lewin’s header deflected out there was no equaliser.

The contest had opened up. Suddenly Eric García was curving a ball along the left to Mahrez as City upped pace and so opportunity. Soon they had a second goal, with this one straight from the Guardiola playbook. De Bruyne passed to Foden, who found Mahrez, who in turn played in Jesus and he calmly finished low past Pickford.

City were coasting but then Bravo added to the catalogue of howlers by passing direct to Richarlison. From here there was an inevitability about how the No 7 would bundle home Theo Walcott’s deflected attempt.

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Guardiola defended the Chilean. “It happens when you play that way but thanks to him [continuing to pass out] you can make a buildup better.”

At the close Calvert-Lewin upended Fernandinho. The managers disagreed as to whether the booking the foul received was sufficient punishment but it did not affect the outcome.