Bernardo Silva broke the deadlock to get City up and running in the 16th minute but the reigning Premier League champions took their foot off the gas after that early opener, with Callum Wilson levelling things up one minute before halftime.
That equaliser jolted City into life. They came out for the second half with added impetus and were soon back in front through Raheem Sterling -- his seventh goal in seven games against Bournemouth.
City then turned on the style to complete the victory, with David Silva and Leroy Sane combining to create an easy chance for Ilkay Gundogan to finish -- the 22nd goal City have scored during this winning league run of six.
With their unbeaten league run now at 20 games, stretching back to April, City are looking in imperious form, while a fourth consecutive league defeat for Bournemouth sees them drop to ninth.
"A good win; after the Champions League it is always tough," City manager Guardiola said. "People think it's easy for us but that is not the truth so I like to win in this way."
Guardiola, with a tricky trip to Watford to come on Tuesday, gave Sergio Aguero a rest and it looked like that decision might backfire with Bournemouth having some promising openings early on.
City soon found their feet, with Bernardo Silva on hand to fire the loose ball into the net after Bournemouth goalkeeper Asmir Begovic could only parry Sane’s effort.
All the possession remained with City but their intensity levels dropped off and Wilson deservedly equalised just before halftime, powering a header past City goalkeeper Ederson.
Whatever Guardiola said at the interval did the trick as City started the second half at a blistering pace, with Sterling soon restoring their lead by firing into the roof of the net after Danilo’s effort had been saved.
City stayed in control, with their fine third goal, finished off by Gundogan, coming after a series of further openings, leaving Bournemouth wondering what might have been.
"Our plan worked, the ball just didn't bounce our way,” Bournemouth manager Eddie Howe said. "This is the closest we have come here."
(Reporting by Peter Hall; Editing by Clare Fallon)
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