The Cherries started the day in second thanks to the longest unbeaten run in the English top flight. But Norwegian striker took his tally to 13 Premier League goals in 10 games.
Haaland's relentless streak is maintaining City's title challenge as they reduced the gap to leaders Arsenal back to six points and edged one point ahead of Liverpool, who they face next weekend. Pep Guardiola remained confident his side can pose a threat to Arsenal come May.
There were more encouraging signs for Guardiola as Rayan Cherki and Phil Foden shone in creative roles, while Nico O'Riley became the first City player other than Haaland to score in the Premier League for over a month. Buoyed by their unbeaten streak since losing at Liverpool on the opening night of the season, Bournemouth played quite good and brightly.