We defended our lead effectively and could have added to it in stoppage time, Azpilicueta and Werner both missing the target when well placed, but a gritty, patient showing with a touch of class when it mattered ensures we will be taking all the points back down the Fulham Road.
We are on our travels again on Tuesday night, further afield at Leicester City. The Blues will head to the King Power full of confidence.
Chelsea (4-3-3): Mendy; Azpilicueta (c), Thiago Silva, Rudiger, Chilwell; Kovacic, Jorginho (Abraham 65), Mount; Ziyech (Hudson-Odoi 75), Giroud (Werner 75), Pulisic.
Unused subs Kepa, James, Emerson, Gilmour.
Scorer Mount 78
Booked Ziyech 72, Thiago Silva 82, Azpilicueta 90+3
Fulham (3-4-3): Areola; Aina, Andersen (c), Adarabioyo; Tete, Reed, Anguissa, Robinson; Decordova-Reid (Kamara 83), Cavaleiro (Onomah 79), Lookman.
Unused subs Rodak, Hector, Odoi, Kebano, Ream, Bryan.
Booked Decordova-Reid 69
Sent off Robinson 44
Referee Peter Bankes