This competition was perhaps City’s only way of salvaging a desperately disappointing season, and after weathering a quick start from the hosts, Pep Guardiola’s men started to threaten an opener.
Erling Haaland headed wide from Matheus Nunes’ cross, shortly before the Norwegian was presented with the chance to break the deadlock from the penalty spot.
Tyler Adams’ handball gave him the opportunity, but Haaland fluffed his lines as Kepa Arrizabalaga made a brilliant save to his left.
Haaland squandered another big chance when chipping over the bar after being played through one-on-one, and those misses came back to haunt City just before the half’s midway point.
The visitors lost the ball in their own third, and Bournemouth moved quickly, with David Brooks’ cross from the right met by Justin Kluivert at the back post, whose limp shot was trickling over the line before Evanilson made absolutely sure by ramming home his second goal in as many games against the visitors.
Guardiola introduced Nico O’Reilly at the break, and the academy graduate immediately had an impact, bursting down the left to square for Haaland who tapped in an equaliser at the back post within four minutes of the restart.
City were dealt a blow when Haaland was forced off injured on the hour, but substitute Omar Marmoush wasted no time in making his presence known.
Within two minutes of his introduction, the Egyptian completed the visitors’ comeback, prodding home after O’Reilly had dispossessed Antoine Semenyo.
Marmoush then had a header cleared off the line by Marcos Senesi as Andoni Iraola’s men scrambled to stay in the contest. While they climbed off the ropes, the Cherries struggled to venture forward, and only the width of the woodwork kept them in the tie as İlkay Gündoğan struck the post.
James McAtee was denied by Arrizabalaga in stoppage time, but Bournemouth’s last-ditch defending could not be built upon by their attack as they missed out on a first-ever FA Cup semi-final.
A 20th H2H defeat from 22 meetings means their attention turns to qualifying for Europe, while City will meet Nottingham Forest in the semi-final as they look to avenge last year’s defeat in the final.
Flashscore Man of the Match: Nico O’Reilly (Manchester City)