De Bruyne fired over from 20 yards when he could so easily have buried a second, but City wasted little time adding their third.
Navas’ persistence paid off when he reached an over-hit pass to keep the ball in play and stand up a cross to the far post.
Aguero did the rest, out-muscling and out-jumping the Bournemouth defence to loop a header back across goal and over the bamboozled Artur Boruc.
Fernandinho hit the bar from 20 yards with Boruc beaten again, before Bournemouth finally rallied.
Steve Cook’s glancing header forced Willy Caballero into his first meaningful save of the day from Matt Ritchie’s teasing cross as the hosts at least fought to make a fist of things.
City took their foot off the gas after the break, doubtless eyeing Wednesday’s Champions League last-eight first leg in Paris.
Pellegrini withdrew De Bruyne before the hour, and Silva just after it.
Eunan O’Kane scuffed a shot badly wide when through for Bournemouth, and City wasted several half-chances, before Kolarov fired an unstoppable fourth for the final word.