Consigned to their first trophyless campaign under Pep Guardiola since 2016/17, City looked determined to bounce back from Saturday’s FA Cup final defeat, as they started brightly against their mid-table visitors.
The Cityzens’ early pressure paid dividends, with Omar Marmoush firing a spectacular 30-yard strike into the top corner for his seventh league goal since moving from Frankfurt in January.
Armed with the momentum, City should’ve extended their lead shortly after, only for Kevin De Bruyne - making his final appearance at the Etihad - to inexplicably hit the bar from point-blank range after good work from Marmoush.
Grateful for the reprieve, Bournemouth came within inches of finding a leveller against the run of play, as Evanilson’s effort on the stretch rebounded off the far post.
That miss proved to be costly, with City doubling their advantage in the 38th minute through Bernardo Silva, who clinically swept home from Ilkay Gundogan’s cut-back.
Faced with a two-goal deficit, the Cherries looked to up the ante at the start of the second half, but clear-cut openings came at a premium with Antoine Semenyo firing wastefully wide from the edge of the box.
The visitors’ hopes of a comeback were given a huge boost with 23 minutes remaining, however, as Mateo Kovacic was shown a red card for bringing down Evanilson as the last man.
Bournemouth’s numerical advantage was short-lived, though, with Lewis Cook dismissed just seven minutes later for a reckless challenge on substitute Nico Gonzalez.
That allowed Guardiola’s men to ease through the closing stages, as Rodri made his long-awaited return from injury and Nico curled home a sublime third in the 88th minute.
Despite a stoppage-time consolation from Daniel Jebbison, City secured an eighth consecutive home victory in the Premier League over the Cherries to close in on a top-three finish.
Flashscore Man of the Match: Omar Marmoush (Manchester City)