Chelsea ground out their third Premier League win in a row after beating Fulham.
Cole Palmer was influential for the Blues once again and slotted home the decisive penalty from 12 yards after Raheem Sterling was brought down by Issa Diop.
The visitors piled on the pressure late on but were unable to find an equaliser.
The result marked a step in the right direction for Mauricio Pochettino and his side in the wake of their shock Carabao Cup semi-final first leg defeat by Middlesbrough.