Fulham held gamely on but were unable to make significant inroads during a match in which they were denied possession and territory.
If the plan from the visitors had been to keep things tight, they were undone after just five minutes when De Bruyne cut through the centre of the field and delivered a pinpoint pass that Sterling converted.
It was a familiar sinking feeling for the guests, who have conceded seven of their 21 Premier League goals in the first 15 minutes.
Another followed not long after that period was over. Sterling this time was the architect as he was fouled by Joachim Andersen. De Bruyne did the necessary from the spot – their 400th in the league under Pep Guardiola.
City were unable to add to their tally before the break but came out with vigour in the second half as De Bruyne cracked one off the bar. Shortly afterwards, the dangerous Belgian was thwarted by Alphonse Areola after he had gone clean through.
Rafael Dias was culpable of a poor miss from a dangerous De Bruyne delivery, but though Guardiola was becoming increasingly irritated on the sidelines, there was never a serious prospect of City being pegged back.
The Citizens focus will now shift to next Sunday’s Manchester derby, as their midweek match against Marseille in the Champions League is a dead rubber as they have already progressed.