Chelsea took all three points in a disjointed match that did not go without its controversies.
After an opening goal from 18-year-old Joshua King was disallowed in a decision that was heavily disputed by Fulham's bench, Joao Pedro found the back of the net on the stroke of half-time.
The Blues were awarded a penalty early in the second half as Ryan Sessegnon was deemed to have committed a handball offence. Enzo Fernandez buried the penalty to secure his second goal in two games.
There was no way back for Fulham after this as Chelsea eased their way to a 2-0 victory in a much-improved second half.
Here is how the Chelsea Players ranked in their victory:
Starting XI
Robert Sanchez - 6
Whether right or wrong, the Spaniard secured his second clean sheet of the season so far. He made some good saves and distributed the ball relatively well.
Malo Gusto - 7
The Frenchman looked really good against Fulham. He was regularly involved in the attacking phase but also made some vital defensive contributions.
Trevoh Chalobah - 5
The Englishman was far from his best today. He got away with one after King's goal was disallowed. The defender just looked a step off the pace for a lot of the match.
Tosin Adarabioyo - 6
Tosin was slightly sluggish at times in this match, but certainly held his own in the Chelsea backline. Not a bad performance against his former employers.
Marc Cucurella - 7
As is often the case, the Spaniard put in another fine performance on the left side of defence. He was defensively solid and tried to contribute further up the pitch when possible.
Moises Caicedo - 8
Yet again, Caicedo was the standout player for Enzo Maresca's men in this match. Had a slightly difficult start but responded fantastically, soon establishing control of the centre of the park. Made a superb block to deny Castagne.
Enzo Fernandez - 7
The midfielder had a really slow start in this one, lacking that creative touch that he so often has. However, Fernandez quickly kicked back into gear, delivering the ball into the box for Pedro's opener and dispatching his spot-kick.
Estêvão - 6
Had a quiet start to the match, but did get some joy as the half progressed. The Brazilian looked like a threat every time he got onto the ball, but the problem was that he did not get as much possession as he would have liked. Nevertheless, very encouraging once again from the 18-year-old.
Joao Pedro - 8
Despite a mostly quiet first half, Pedro still found himself on the scoresheet, once again proving a threat from set pieces. He was much more involved in the second half, being the focal point for a lot of Chelsea's attacks.
Pedro Neto - 6
He has had better days in Blue for sure, struggling to have any sort of impact on play in the opening 45 minutes. Grew into the game, especially in the second half, but would have been hoping to test Fulham's backline more than he did.
Liam Delap - N/A
It would be harsh to judge Chelsea's number nine after he went down in the 12th minute with a hamstring problem.
Substitutes
Tyrique George - 5.5
Did not see much of the ball at all during his time on the pitch. Playing centrally today, George struggled to impact play. He did test Leno on one occasion, giving the German something to think about in that first half.
Jamie Gittens - 5
Not a great cameo from the winger who only managed six touches of the ball in the 22 minutes he was in the game.
Reece James - N/A
Came on in the 81st minute. He did not really have sufficient time to influence the game.
Andrey Santos - N/A
Came on too late to make a fair judgment.