Palace, meanwhile, had yet to pick up a point or even score a goal in the Premier League, and had already sacked Frank De Boer to introduce Roy Hodgson at Selhurst Park.
After the Palace match at the Etihad Stadium on Saturday, City host Shakhtar Donestsk in the Uefa Champions League on Tuesday before visiting reigning champions Chelsea ahead of the October global break.
But right on half-time City made the breakthrough as a clever chip from David Silva was controlled by Leroy Sane. His break down the left flank was picked out by De Bruyne and a ideal low cross into the path of Sterling meant the England winger could not miss.
An impressive 16 goals have come from those five matches with Sergio Aguero in his usual great form.
Just one to go for Sergio.
Liverpool won 3-2 at Leicester City in typically heart-in-the-mouth style when Simon Mignolet comically conceded and then saved a late penalty, which Jamie Vardy fired too close to the Belgian's body. The same could be said for the weekend before when they succumbed to Burnley 1-0 in a game they really should have taken at least a point from.
Pep Guardiola was spotted giving a team talk to a ball-boy at 38 minutes.
Holding onto Coutinho is proving to be a wise decision for Liverpool
Aguero had to wait until the 79th minute for his obligatory goal.
Crystal Palace, in contrast, are struggling massively and have failed to win a single game so far in the Premier League, failing to score.
Step forward Roy Hodgson.
Hodgson surely has some work on his hands to quickly find an adequate replacement to lead the Palace attack and who can produce the goals to help keep them in the top-flight. "Everything was slow. Anything can happen". "The second half we were at the level of the last few weeks".
"When we get into positions we are making more of the right decisions".
"I like the strikers who play in the process, like I don't just like the central defenders to defend". Gabriel is an awesome player. "I knew at that point it was going to be my destination". They are now odds-on at 4/5 to go down. We have to create the game.
City continued to dominate and Fernandinho had a decent opportunity in the area on 13 minutes but fired his effort straight at Wayne Hennessey, before Sterling was denied moments later. "That is why I am in love with him for different reasons". "The feeling I think is a little bit better, but it's just September". He was ably supported by those around him, with Kevin De Bruyne putting in a dominant midfield display behind a wealth of attacking talent.