A second-half penalty calmed Chelsea's nerves after Conor Gallagher was sent off just before half-time.
The Blues had been in control, taking an early 2-0 lead through two far-post headers from Fernandez and Levi Colwill, the latter of whom scored his first goal for his boyhood club.
Mykhailo Mudryk won the spot-kick to help 10-man Chelsea over the line in a potentially difficult second half, despite Joao Pedro pulling one back in stoppage time.
Nizaar Kinsella was at Stamford Bridge to rate the Chelsea players.
Robert Sanchez - 7
Exorcised his demons after an unconvincing Carabao Cup display against Brighton, playing much better against his former club this time around.
Axel Disasi - 6
Got the better of Simon Adingra in the first half, but struggled more with Kaoru Mitoma.
Thiago Silva - 8
Came into his own in the second half, making some unbelievable tackles as Chelsea defended their lead.
Benoit Badiashile - 7
Put his poor performance last week behind him, defending well and setting up Fernandez's opening goal.
Levi Colwill - 7
Well-timed leap allowed him to score his first Chelsea goal against his former loan club, but couldn't stop Facundo Buonanotte as he pulled one back before the break.
Moises Caicedo - 5
Lucky not to be sent off, flying into tackles after earning a yellow card for dissent.
Enzo Fernandez - 8
Fernandez silenced the doubters with his first Premier League goal through a headed finish, almost adding a similar second moments later. Also cooly dispatched a second-half penalty.
Conor Gallagher - 4
Can have a few complaints after diving into challenges and earning two yellow cards to get sent off; that's poor discipline.
Mykhailo Mudryk - 7
Started slow but the 22-year-old winger got his eye in with a long-range shot at the end of the first half before winning a penalty through his pacy direct running.
Nicolas Jackson - 6
Made some nice touches early on and set up Colwill's header but didn't look like a goal threat.
Raheem Sterling - 8
Increasingly becoming Chelsea's talisman and they looked to him at every opportunity to hit Brighton on the break.
Cole Palmer - 6
Left out due to a minor knock, the forward came on with a lead to protect and kept it simple.
Ian Maatsen - 6
The Dutchman helped Chelsea hold firm as a disciplined right-wing presence.
Armando Broja - 6
The late substitute barely touched the ball but he was a suitable outlet.
Unused subs: Petrovic, Bergstrom, Madueke, Deivid, Gilchrist, Matos