The home side were quickest off their blocks with Harry Wilson forcing David Sanchez into a save in the second minute before the Blues hit the crossbar in the 19th minute after an Andrey Santos header.
However, Marc Cucurella was sent off three minutes later for pulling goal bound Wilson to increase the pressure for the visitors.
Fulham soon had the ball in the net from Wilson at the stroke of half time, but a VAR check ruled the goal out due to an offside in the build-up.
The Cottagers continued to threaten after the break and were rewarded when Raul Jimenez latched onto Sander Berge cross to score the opener in the 55th minute.
Chelsea began to come back into the game with Liam Delap coming close in the 63rd minute after a Cole Palmer dummy but eventually found an equalizer after Fulham failed to clear their lines from a corner.
A determined Harry Wilson added a second goal for the home side in the 80th minute with the Blues failing to find an equalizer and condemning them to their fourth ever loss against Fulham in the Premier League era.
"I'm really proud of the performance but we have to talk about it in different ways," said interim manager Callum McFarlane, who was in charge of Chelsea for the match with newly appointed Liam Rosenior watching from the stands.
"We had just got into our rhythm, had a couple of set-pieces, but we got countered and went down to 10 men.
"We had moments and I was really proud of the character to get back in the game. We didnât look like conceding again until a bit of quality from Harry Wilson that decided the game. So, weâre disappointed," concluded McFarlane.
Meanwhile, Fulham head coach Marco Silva praised in-form matchwinner Harry Wilson for his performance.
"He's been incredible," said Silva.
"Right now, everything he touches becomes something magic, something that will have an impact. You just have to try to take the best from him."
The result sees Chelsea drop to eighth spot on the league table whilst Fulham move up to ninth.