Emile Smith Rowe capitalised on a Chelsea mistake to score the only goal of the game, and extend our winning run in the league to three games.
Having scored his first ever Premier League goal at the weekend against West Brom, he netted again in the derby to set us on the way to a hard-earned three points.
This goal owed a bit more to good fortune though, as he stroked home from Pierre-Emerick Aubameyang's pass, once Chelsea keeper Kepa Arrizabalaga had scrambled back to prevent an own goal.
For much of the rest of the game it was about resolute defending, right from the front back to our five-man defence.