On a blustery last night, Pep Guardiola's side closed the gap on Chelsea to eight points and kept alive their hopes of the title, despite their Spanish manager ruling out the possibility following his team's 4-0 defeat at Everton last month.
But three league wins in a row have reignited City's season with FA Cup and Champions League games to come in the next eight days as Sergio Aguero issued a timely reminder of his attacking prowess after coming on as an early substitute for the injured Gabriel Jesus.
He said they would only know the extent of Jesus' injury on Tuesday.
"Hopefully it won't be for a long time -- I will pray tonight -- we will have to wait until tomorrow," said the 46-year-old, who refused to accept the title was still on as the gap to Chelsea he said was still 'massive'.
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His Bournemouth counterpart Eddie Howe has seen his side's form deteriorate since the turn of the year -- they are yet to win in 2017 and lie only six points above the relegation zone.
City fans hoping to see Jesus add to his scintillating start for the club were disappointed as the Brazilian lasted only 14 minutes before being replaced by Aguero after turning his ankle.
It gave Aguero an opportunity to show some form amidst speculation he could be regarded as surplus to requirements with the arrival of Jesus.
A swift one-two between Jack Wilshere and Jordon Ibe saw the latter through on goal but goalkeeper Willy Caballero smothered the ball with his legs.
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Bournemouth then suffered a blow when their captain, Simon Francis, who had been doubtful for the match, left the field to an injury.
City almost went ahead immediately after that when Leroy Sane crossed for Sterling whose shot was deflected onto the post by Steve Cook.
Sterling could not believe his luck but he did not have long to dwell on his disappointment.
Just three minutes later, Sane crossed again and this time Steve Cook deflected the ball into the path of Sterling who smashed in at the far post for his fifth Premier League goal against Bournemouth, the most he has scored against a single opponent.
Bournemouth felt aggrieved though they had City rattled and, when Jack Wilshere also withdrew through injury, Howe replaced him with Benik Afobe, a striker as he sensed an opportunity.
Though City continued to impress on the break, with Sane in particular causing the Cherries problems, Bournemouth kept threatening.
Afobe passed to Harry Arter whose curling shot was tipped round the post by Caballero following some neat approach work from the home side.
However, City went down the other end and killed it off as a contest.