The Germany international scored early in each half as Thomas Tuchel’s side closed in on a top four finish.
Chelsea remain in fourth position in the table and move six points clear of nearest rivals West Ham United, having played a game more.
The result also edges Fulham closer to relegation as they stay in 18th and nine points from safety with four matches remaining.
The pair combined again moments later with Havertz putting the ball in the back of the net but the goal was ruled out for offside.
The hosts doubled their lead three minutes into the second half when Timo Werner and Havertz combined with the latter grabbing his second of the game.
Havertz and Werner both had chances to grab a third but Chelsea comfortably saw out the rest of the game to secure a crucial win in their bid for Champions League qualification next season.