Poacher Aguero threw himself at the ball to score that 100th home league goal with a diving header. Bournemouth had a spell before half-time when they suddenly troubled the league leaders.
Much of that, though, was caused by City being careless at the back – but it was a more purposeful, switched-on Blues at the start of the second half.
What boss Pep Guardiola had to say at halftime, no doubt, was a factor there. And City increased their lead in the 53rd minute with Sterling again on target.