A weakened and slightly laboured Manchester City still managed to open a five-point gap at the top of the Premier League, a warning to the rest of the competition that, even with big names missing, they can keep up their scoring average of three goals per game. City do function better, however, when David Silva is involved and, though the Spain midfielder came on for only the last 13 minutes, it was enough to make the point.

“We were flat at times but that’s normal when you play a lot of matches,” Pep Guardiola said. “I’m still delighted with the win, because one or two big teams will drop points this weekend. Maybe we weren’t good for the whole 90 minutes but we did enough in 75 to win the game. I don’t know what Leroy Sané ate before the game but I am going to show him the video and try to get him to eat it again. Next time he complains about not playing, I’ll tell him if he plays like that he will be in the side.”

Guardiola rested several key players following City’s midweek exertions against Lyon, though the home side retained enough pace to trouble Bournemouth in the form of Sané and Raheem Sterling on the flanks. The former was particularly effective in the first half, regularly running on to well-struck passes from Ilkay Gündogan or Oleksandr Zinchenko to find space in behind Bournemouth’s flattish back five.

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The first goal arrived in just such a manner, Zinchenko aiming a ball into the penalty area for Sané to attempt to reach first. The winger managed to stay onside and sprint clear of the Bournemouth defenders and, though Asmir Begovic left his line to try to cut out the danger, he was unable to make a clean catch because Sané was in such close attendance. Begovic succeeded in clearing the immediate threat from Sané but only at the expense of pushing the ball to Bernardo Silva, who unhesitatingly swept the ball into the unguarded net from close to the penalty spot.

Ederson, in the City goal, is currently rivalling David de Gea at Old Trafford for minutes spent merely watching games without being directly involved, but like his counterpart at Manchester United he keeps up his concentration so as to be ready when called on. Bournemouth might have equalised a few minutes before Callum Wilson brought them level when the same player got on the end of a Josh King cross, though his touch was hardly emphatic and the hitherto unemployed Ederson made a sprawling save. Wilson made amends for the miss a minute before the interval, this time getting above Nicolás Otamendi and Danilo to meet Simon Francis’s cross and give Ederson little chance with a firm and well placed header.

Facebook Twitter Pinterest Callum Wilson climbs above two Manchester City defenders to head Bournemouth level just before half-time. Photograph: Paul Ellis/AFP/Getty Images

Turning round level was no more than Bournemouth deserved. City had enjoyed more than two thirds of the first-half possession but without David Silva seemed short of ideas of how to use it. Gabriel Jesus was inconspicuous as an attacking spearhead, and too many of the home side’s attempted attacks broke down on the edge of the area. Bournemouth gradually clawed their way back into the game as if surprised at how lightly they were being allowed to get off.

As Ryan Fraser and Andrew Surman started to pass the ball around City’s 18-yard line, gaps appeared and, as the interval approached, Bournemouth were attacking with the sort of conviction that eventually brought a reward.

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Eddie Howe’s team began the second half brightly too, with Wilson straight away getting ahead of Aymeric Laporte to set up a chance for King. City went down the field to hit the post at the other end, Sterling ending an adventurous dribble with a slightly tame shot that deflected off Steve Cook to strike an upright. Undeterred, Sterling started and finished City’s second goal just before the hour, first setting up Danilo for a shot, then moving up to tuck away the rebound when the winger’s effort was blocked by a combination of Begovic and Nathan Aké.

Even when back in the lead City showed signs of easing up again, so Guardiola sent on David Silva just to be on the safe side. It was a shrewd move. The substitute had been on the field precisely two minutes when he came up with the pass of the match, freeing Sané to cross from the goalline and leave Gündogan an easy close-range finish. “City have individuals who can hurt you but I thought the goals were scrappy from our perspective,” Howe said. “I think that’s the closest we’ve come to matching them. At least we managed to limit them in terms of clear-cut chances.”