Raheem Sterling opened the scoring before an own goal from Tyrone Mings handed City victory as Pep Guardiola's side cut Chelsea's healthy advantage to eight points.
The opener arrived after teenage sensation Jesus, fresh from three goals in his first two top flight starts, departed with a foot problem.
Sergio Aguero has been consigned to the bench by the Brazil international, with speculation over his long-term future at City an inevitable by-product of his demotion.
City's top scorer was denied a 19th goal this season when Mings was ruled to have got the more decisive touch to Sterling's 69th-minute cutback but the Argentina star could now have a prolonged opportunity to regain his position as the club's first-choice striker.
Bournemouth remain without a win in 2017 and, having lost Jack Wilshere to injury during the match, boss Eddie Howe will view the six-point gap between his side and the relegation zone with increasing trepidation.
The latest twist in the Jesus-Aguero narrative came inside the first 15 minutes as the Brazil star landed awkwardly when attacking a cross from the right.
He removed his boot to receive treatment on the field before hobbling off, with Aguero afforded a hero's welcome from the travelling supporters.
City goalkeeper Willy Caballero was off his line quickly to make a vital sliding block on Jordon Ibe, a scare that prompted Guardiola's men to shift through the gears.
Sterling saw his 26th-minute shot spin off a sprawled Steve Cook and against the post, with Charlie Daniels blocking Kevin De Bruyne's follow-up.
Yaya Toure then curled a left-footed effort narrowly wide from 25 yards and the pressure told before the half-hour – a Cook deflection from David Silva's low cross this time working in Sterling's favour to leave the England man with a simple finish.
Bournemouth thought they had an instant equaliser but Josh King was correctly penalised for pulling back John Stones before converting.
City were unable to double their advantage before the break as Aguero blazed wastefully over from Bacary Sagna's right-wing centre and a hefty casualty count climbed further in first-half stoppage time.
Having already sent on Mings in place of Simon Francis, Howe faced the worrying sight of Wilshere failing to shake off the effects of a challenge on the excellent Silva.
Benik Afobe came on in Wilshere's place and the home supporters were furious when the already booked Toure brought down the substitute.
Guardiola's men were forced to ride out some early second-half pressure before City got back on the front foot – left-winger Leroy Sane ensuring a thorough working over for Adam Smith was not consigned to the first period.
But the open nature of the contest remained to Bournemouth's liking and Caballero was down sharply to his right to keep out Harry Arter's rasping left-footer.
The sense of City requiring a second was palpable and Aguero was to the fore when it arrived.
The final touch came off the Mings as both men lunged at a Sterling's cutback, the opening goalscorer having danced around an increasingly beleaguered Smith.
Six minutes from time a mistake by Mings allowed Sane to beat Cook and thrash goalwards, but the crossbar denied him the goal his effort deserved.