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.
"I think it was very important. We have to come in the top four of the Premier League, that is our goal for the season and this win today is crucial for us. Then, on Wednesday we have another important game so we're happy with the win," Havertz said after the game.
Chelsea manager Thomas Tuchel praised Havertz's performance after the club's 1-1 draw against Real Madrid earlier in the week in Champions League semifinals play.
"Still there's room for improvement but today I'm very happy. He was decisive and involved in dangerous attacks and situations. To have players on the pitch who maybe had a tough decision against them on Tuesday [vs. Madrid], but he took his chance and showed up and that's what we need all the time," said Tuchel.
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.
Tuchel also praised Mount's play: "He has the full package -- mentally, talent and physically and his character. He has both feet on the ground - he's a nice guy. I have the feeling he comes to Cobham to learn and get new experiences."
Meawhile, Fulham manager Scott Parker knows his side has a big hill to climb to avoid relegation.
"We'll try to win four games now that's the aim and we have to try to do it. I'm proud of the team and the performance. In certain moments we lacked in certain areas," said Parker.