The Ivory Coast international scored twice in the opening half before clinching a well-earned hat-trick with Chelsea's fifth.
Kalou was supported by a double from Frank Lampard and goals from substitute Daniel Sturridge and Florent Malouda.
The Blues now face Liverpool at Anfield on Sunday in what could be a pivotal moment in the title race and Kalou maintains the victory over Stoke showed how badly Carlo Ancelotti's squad want to be crowned champions.
Winning 7-0 at home shows we really want to be champions, said Kalou. If you want to be champions, that's the kind of game you have to win.
We didn't show any nerves. Everyone was at their best and played very...