By Chris Bevan
BBC Sport at Etihad Stadium
Bournemouth are still three points adrift of Premier League safety with two games remaining after their recent revival ended with a battling defeat at Manchester City.
After the Cherries had seen a series of chances come and go, David Brooks' late strike gave them the hope of an unlikely point at Etihad Stadium but they fell short of another comeback to boost their fading survival hopes.
David Silva had put City ahead with a superb free-kick after just six minutes, curling in from the right-hand corner of the box via the underside of the bar.
Pep Guardiola's side had scored five times in each of their previous two outings but, in their first game since learning their European ban has been overturned, they did not seem in the mood to punish their opponents further.
Instead it was Bournemouth, fresh from their remarkable comeback to beat Leicester at the weekend, who threatened a repeat of that recovery here.
The visitors went close in the first half when Ederson had to push Junior Stanislas's whipped free-kick on to his post, and was fortunate when the ball bounced back off his head and out of play.
Soon afterwards, City's Brazilian goalkeeper needed the help of Nicolas Otamendi to deflect Dominic Solanke's goalbound shot over the bar, and Philip Billing headed over from the resulting corner.
Bournemouth were on top and appeared full of confidence, but they were left to rue their wastefulness in front of goal when Gabriel Jesus struck City's second before half-time.
There were five defenders around Jesus when he collected David Silva's pass inside the box but he beat two of them with a step-over and a dart into space before planting his shot into the bottom corner of the net.
Even then, the Cherries were not done but when they did get the ball in the City net after the break, it was ruled out for the most marginal of offsides.
Stanislas cut back inside the box and bent the ball past Ederson but Joshua King was flagged offside after applying the final touch at the far post, and the video assistant referee confirmed the decision by the width of his big toe.
It appeared City would get the chance to wrap things up from the spot when Lee Mason awarded them a penalty for Steve Cook's tackle on Jesus, but VAR overruled his decision.
That gave Bournemouth fresh hope and Brooks set up a frenetic finish when Callum Wilson burst forward and found Brooks clear in front of goal to slot home.
The duo combined again deep in injury time, but Wilson saw his shot roll wide and his side's hopes of salvaging a point were over.
Coverage of Wednesday's Premier League action Lawro's predictions v DJ & Aston Villa fan Nathan DaweMore to follow.