The Blues defeated the newly-promoted Brentford, thanks to Ben Chilwell’s 45th-minute strike.
The win over Brentford means Chelsea have now become the first club from the English capital to win seven consecutive away London derbies in English Football League history.
Chelsea are now on top of the Premier League table with 19 points from eight fixtures.
Thomas Tuchel’s side are one point ahead of second position Liverpool and two points ahead of third-place Manchester City.
Chelsea will tackle Malmo on Wednesday in a UEFA Champions League tie at Stamford Bridge.
Meanwhile, Chelsea have been backed by a former Manchester United captain, Gary Neville, to win the Premier League title this season.
Tuchel’s side finished in the fourth position last season behind Liverpool, Man United and Man City.
