Chelsea lined up with three of their eight January signings, including starting British record transfer Enzo Fernandez just 72 hours after arriving from Benfica as well as Benoit Badiashile and Mykhailo Mudryk.
But the lowest scorers in the Premier League's top 10 again lacked a cutting edge in attack to leave them in ninth place in the table but now having played at least one game more than the teams below them.
Fulham's impressive season continues, meanwhile, as they move up to sixth place, two points above their local rivals but having played a game more.
"Within the team there's a good feeling," Chelsea boss Graham Potter said. "Within the game I agree we didn't do enough in terms of our attacking play to create more, which is something we need to do.
"I think you saw a team against us that defend very well, very organised. That bit of connection and understanding that you need we probably lacked a little bit which is understandable given we have players coming back from injury and new players in the team. So that's just where we're at at the moment.
"Some positive for us of course. The effort was there, the spirit was there, but as an attacking team we would like to do more."
As well as Chelsea's new signings, there was also a welcome return from injury at right-back for Reece James and a surprise place for winger Hakim Ziyech just days after his deadline-day move to Paris Saint-Germain fell through at the last moment.
But Potter's side, having scored just 22 goals from their first 20 games, again struggled to present a consistent attacking threat. Fernandez, though, was a bright spot and at the heart of most of the hosts' best attacking moves in the opening half.
The World Cup winner's lofted pass in the 32nd minute sent Mason Mount clear down the left and only a crucial touch from Tim Ream likely prevented Kai Havertz from putting Mount's low cross on target.
- O'Halloran: Chelsea's attacking woe overshadows Fernandez debut
A few minutes later another Fernandez pass released Ziyech running into the box down the right but the Morocco international's effort was sliced wildly wide of the Fulham goal.
It was Havertz, again looking unconvincing in the No. 9 role, who had the best chance to break the deadlock in the opening half but, clear through on goal, his lofted effort over Fulham goalkeeper Bernd Leno struck the post.
At the other end, Fulham, who won the reverse fixture 2-1 just three weeks ago, began to grow into the game. And Andreas Pereira went close with a low shot that had Kepa Arrizabalaga diving at full stretch to keep it out.
Fulham gave as good as they got in the second half, too. Willian looked in inspired mood against his former club, forcing Kepa into a save at the start of the half and creating another opening soon after for Pereira.
And Fofana nearly provided it with 11 minute remaining. The Ivorian striker rounded a stranded Leno on the edge of the box but Ream got back to make a sliding clearance off the line to save a certain goal and a share of the points.
"It's a team game. We work on it every week," Fulham captain Ream told Sky Sports. "Defend from the front and attack from back. It takes all 11 guys and the ones coming on."
- Stuart Attwell
|Brighton & Hove Albion||5||4||0||1||+8||12|
|West Ham United||5||3||1||1||+3||10|