Chelsea, who headed into the game on the back of their 1-1 draw with Manchester United last weekend, raced into a three-goal lead thanks to strikes from Diego Costa, Pedro and Willian at Stamford Bridge.
Pedro then made it 4-0 shortly after half-time, before substitute Bertrand Traore added a fifth late on.
Andros Townsend then scored a late consolation for the visitors, who failed to click into gear in west London.
The result left Chelsea in 12th place in the Premier League table and 14 points behind fourth-placed Manchester City heading into the final 12 games of the season.
Pedro and Radamel Falcao were among the Chelsea players to take to Instagram after the game – and here are some of our favourite updates.
Pedro Rodriguez: “Great game by the team today. Happy with the goals and winning confidence for upcoming challenges. Come on Blues!! #CFC @chelseafc”
Radamel Falcao: “Great game today!. Congratulations team. Great job.”
Cesar Azpilicueta: “Great game and great result! Now focus on Champions league! @chelseafc #cfc #premierleague”
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