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Three days after joining the Blues for a staggering £106.8 million ($186 million) Premier League record fee on transfer deadline day, Fernandez made a tidy first appearance for his new club but was unable to celebrate with a win.
Big-spending Chelsea lacked a cutting edge, with Kai Havertz hitting the post in the first half of a stalemate at Stamford Bridge.
A point keeps Fulham above the Blues in the table and struck another blow to its neighbour's hopes of securing a top-four finish.
Chelsea was disjointed in the first half with a new-look side needing time to gel and Andreas Pereira almost put Fulham in front with a powerful right-footed drive that was tipped around the post by Kepa Arrizabalaga.
Tim Ream got a slight touch on Mason Mount's pass to prevent Havertz from converting at full stretch and the Germany international endured more frustration just before the break.
Hakim Ziyech, who saw a deadline-day move to Paris Saint-Germain fall through, picked Havertz out with a brilliant pass and his lob over Bernd Leno came back off the post.
Mykhaylo Mudryk was replaced by fellow new boy Noni Madueke at half-time after a disappointing first start, but Chelsea continued to lack fluency.
Fernandez was just off target with a long-range right-footed strike after an audacious attempted lob from Aleksandar Mitrovic had Kepa scrambling back to claim on his line.
Conor Gallagher fired wide and Ream cleared David Datro Fofana's shot off the line after he rounded a stranded Leno on a frustrating evening for Chelsea.
