Enzo Fernandez made his Chelsea debut after becoming the most expensive player in British football history with a £107 million move ($132 million) from Benfica on transfer deadline day.
Mykhailo Mudryk was also given his Stamford Bridge bow, while Noni Madueke and David Datro Fofana came off the bench for their Premier League debuts.
Chelsea's record investment of over £300 million in the January window took the total spend on new players in their first season under new ownership to over half a billion.
Co-owners Todd Boehly and Behdad Eghbali were in attendance, but will not have been impressed as another chance to close on the top four slipped by.
Graham Potter's men sit ninth in the table, still nine points adrift of the Champions League places.
Fulham had secured a first victory in the west London derby since 2006 when the teams met just three weeks ago.
Marco Silva's men sit two points and three places above their local rivals in the table in their first season back in the top flight.
Fulham were seeking a first ever league double over Chelsea and came close to achieving it as Andreas Pereira forced Kepa Arrizabalaga into a flying save low to his right.
For the enormous sums spent by Chelsea's new owners, their lack of a clinical goalscorer was exposed once more.
Kai Havertz had a hat-trick of big chances to break the deadlock before half-time.
The German international failed to get enough contact on Thiago Silva's brilliant pass to divert the ball beyond Bernd Leno.
Havertz then could not stretch to turn Mason Mount's dangerous cross on target.
But his best opening came when he hit the post with a lob over Leno from Hakim Ziyech's defence-splitting pass.
Ziyech would have been a Paris Saint-Germain player this week had Chelsea not submitted the wrong paperwork in the minutes before Tuesday's transfer deadline.
The Moroccan is just one of a wealth of wide options now available to Potter and he wasted no time in hooking Mudryk despite his price tag after a disappointing first 45 minutes.
The Ukrainian joined from Shakhtar Donetsk last month for a fee that could rise to 100 million euros ($110 million).
Madueke was introduced in his place and Potter also threw on Raheem Sterling from the bench on the hour mark in the search for a winner.
Fernandez was inches away from the perfect debut as the Argentine World Cup winner flashed a shot wide from distance 20 minutes from time.
Connor Gallagher came even closer as he hit the side-netting from the edge of the box.
But the best chance fell to Fofana as the Ivorian rounded the stranded Leno, but failed to beat the covering Tim Ream on the line.