The visitors had remarkably trailed in their last six away league games before today, but managed to get their noses in front through Phil Foden.
The Englishman tapped home his fourth goal in as many appearances against the Cherries, after Neto could only parry Erling Haaland’s effort straight into his path.
The pair combined well earlier on, but Haaland could only curl wide after Foden put him through on goal as the champions searched for a second.
Bournemouth’s best chance fell to Milos Kerkez, with the left-back’s fierce strike tipped over by Ederson.
The hosts started the second half much better, and Marcus Tavernier should have done better with a scuffed shot that was headed clear by Rúben Dias, with Ederson helpless on the ground.
The winger then wasted another chance as he skewed wide in space following a nice lay-off from Dominic Solanke.
Bournemouth’s 14-goal striker was also denied by a smart save from Ederson midway through the half, as Andoni Iraola’s side refused to give up.
However, their lack of quality was on show late on, as a number of overhit crosses let City off the hook. One did find the head of substitute Enes Ünal in stoppage time though, but the ex-City man’s effort bounced agonisingly wide in what could have been a memorable home debut for the Turk.
Ultimately, defeat means their winless league run now stretches to seven games as they drop to 14th in the table, while Pep Guardiola’s team move back to within one point of leaders Liverpool in their hunt for an unprecedented fourth consecutive PL title.
Flashscore Man of the Match: Phil Foden (Manchester City)
