This was a slog for Manchester City, but after a fiercely contested game on the south coast against opponents who refused to wilt it should probably be considered evidence that Pep Guardiola’s side will pose the most credible threat to Chelsea’s advantage at the top of the Premier League. City have sprung into second place, taking advantage of the leaders’ slight stutter on Sunday at Burnley and Guardiola could arguably draw more positives from this hard-fought victory than the 4-0 thrashing they had inflicted on West Ham United in their previous away fixture.

That had proved a stroll at the London Sadium but, confronted by opponents yet to win a game in 2017, City had to scrap to impose themselves. In the autumn, once City’s scintillating start to life under Guardiola had petered out, they might have shrunk in the face of the resistance offered by an energetic and eager Bournemouth team.

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Yet they have steeled themselves in recent weeks. A fourth successive win in all competitions in what will be their last league fixture until the first week of March maintained the momentum. This team have been revitalised, with Leroy Sané and Raheem Sterling irrepressible, David Silva and Kevin de Bruyne orchestrating their play expertly from deeper roles, and Sergio Agüero eager to reassert himself as their predator-in-chief.

The Argentinian, who had come on as a substitute for the injured Gabriel Jesus, left the field insistent that he had scored for the first time since early January. Agüero had held off another substitute, Tyrone Mings, as he darted across his marker midway through the second half sensing Sterling would have the beating of Adam Smith down City’s left flank, and stretched out for the winger’s low centre on the edge of the six-yard box. There was a flick on the loose ball, but it cannoned beyond Artur Boruc off Mings as the centre-half desperately sought to get ahead of the striker. He will grumble in frustration to be denied his own reward, but his attacking instinct had still drawn the error. City will await news of the extent of Jesus’ foot injury, sustained in the early exchanges, but know they have a match-winner who is glad to be back.

Agüero should revel at the prospect of slotting back into this front-line in the weeks ahead. Sané, in particular, was magnificent down the left, was unlucky late on when he belted a shot on to the crossbar. His gliding menace contrasted with Sterling’s scuttling energy on the opposite flank.

“People say we only brought in one guy [Gabriel Jesus] in the January transfer window but, since Arsenal [in mid-December], something has clicked with Sané,” said Guardiola. “He’s shown us a lot of things. He is so fast, and his intensity has helped us a lot, and he is only 20.” His potential is frightening.

It had been the German who had dumped Smith on the turf while the game was still goalless, his centre reaching Sterling whose shot was deflected by Steve Cook on to a post. Within minutes, however, that pair had combined once again with Sané’s centre flicking off Cook and evading Charlie Daniels at the far post. Sterling lurked unmarked to convert an eighth goal of the season with ease.

That combination down the flanks, supplied by Silva’s clever slide-rule passes, will propel this team’s late challenge to Chelsea’s dominance at the top. “I thought City were very good and gave a very controlled performance as the away team,” said Eddie Howe. “Our lads gave everything they could, worked incredibly hard, and I can’t ask for anything more. I just felt they were better than us.”

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Howe had no complaints at the referee’s decision to deny Josh King an equaliser after the striker pulled back John Stones in the build-up, and had taken heart from Jordon Ibe’s improved display on a first league start since early November during which the former Liverpool winger almost eased the hosts ahead. Willy Caballero’s outstretched right leg had denied them that privilege.

This was not the performance of a team nosediving into a relegation scrap, their frenetic energy and urgency deserving of better, and they can go into the remaining fixtures with more optimism. Yet the ill-fortune thrust Bournemouth’s way did reflect that of a team enduring a slump in form.

No sooner had Howe found relief in the restoration of his first-choice back-line than Simon Francis suffered a hamstring injury. Jack Wilshere then crumpled to the turf clutching his left ankle after blocking a shot from Silva. The grimace on the Arsenal loanee’s face as the midfielder departed just before the interval looked worryingly familiar.

They will be as anxious about the extent of any damage as City will be over Jesus’ fitness, though at least Bournemouth have time now to lick their wounds before targeting a recovery. City, in contrast, have FA Cup and Champions League ties looming against Huddersfield Town and Monaco. They have moved to within eight points of Chelsea in the championship race, Guardiola still insistent the title is the leaders’ to lose, but their presence leading the chasing pack will keep Antonio Conte on his toes.