City’s victory maintains their 100% home record in the league this season, with eight wins out of eight, but this latest triumph was not as straightforward as the scoreline might suggest.
All seemed to be going to plan for Pep Guardiola’s side when Bernardo Silva smashed them ahead early on, with the Portuguese midfielder following up after Asmir Begovic had denied Leroy Sane.
But the home side, with David Silva on the bench and top scorer Sergio Aguero absent altogether after he complained of a muscle discomfort, relaxed a little too much before half-time and were deservedly punished.
To the displeasure of the home fans, the Cherries were given far too much time and space to build outside the box and Simon Francis swung in a perfect cross for Callum Wilson to rise and head home.
Bournemouth threatened again after half-time when King’s looping cross almost dropped in at the far post, while City looked surprisingly short of urgency or inspiration.
It was Sterling who supplied the spark they were missing, to continue his remarkable run of scoring against the Cherries.
The England forward followed up after Begovic could only parry Danilo’s low shot and Nathan Ake failed to clear, firing into the roof of the net for his 10th goal in seven games against the Cherries.
Bournemouth, looking to avoid a fourth successive defeat, did not lie down and some dangerous balls into the box ensured some nervous moments for the Etihad faithful.
It took Gundogan’s close-range finish to make sure of the points with 11 minutes remaining, with the impressive Sane providing the assist with a precise pull-back.
“[Southampton] are a good side, so strong up front, so we could not press,” Guardiola said. “They played long balls, attacked the channels. They were taller than us and stronger than us.
“In the last 20 minutes we were flat, we did not have the rhythm we needed. Winning that way, we suffered a lot in the first half, especially in the last 20 minutes. That is why I am delighted to win in that way.”
This is the start of a punishing six-week schedule that sees City play 13 games in the space of 44 days, including every midweek and weekend in December.
So it was perhaps not surprising that Guardiola chose to shuffle his squad, with five changes from the midweek draw with Lyon. Although the omission of Aguero was forced upon him.
With seven goals in his past 10 games, the Argentina striker has been in prolific form in recent weeks, and he was the player City missed more than most here.
Before Saturday, City’s attack had been even more lethal than the same stage last season, with more shots and shots on target than in 2017-18.
But their attacks were strangely short of an end product for almost an hour of this game, and the home crowd were beginning to voice their frustration until Sterling struck.
Bournemouth had been beaten heavily on each of their three previous visits to the Etihad, conceding a total of 13 goals.
But Cherries boss Eddie Howe did much better with his approach this time, with his side well organised at the back and frequently breaking forward dangerously too.
“I think it is the closest we have come [to matching Manchester City at the Etihad],” Howe said.
“I don’t know if it is the best we have performed. I still don’t think we have fully delivered a performance that we are truly capable of here but think that is the closest we have come.”
They had already got in some good positions without finding the right final ball when Wilson rose to power his header home, and continued to look dangerous with the score at 1-1.
City are the only Premier League team this season not to have dropped any points this season from winning positions, but that scenario looked a distinct possibility until Sterling struck.
Even then, the Cherries did not crumble. Four successive defeats have taken the shine off Bournemouth’s strong start to the season, but this performance should give them some belief that they can stay in the top half of the table.
“I think we limited them in terms of clear cut chances today and I think the goals came at bad times for us but don’t think we looked too vulnerable,” Howe added.
“Yes, they had a lot of the ball but it was in front of us and we were happy with that. But we had some good moments on the counter attack and a lot of opportunities from set-pieces.
“There were just a couple of moments that just went against us – it’s the closest we have come.”
