The Argentine midfielder headed the Blues in front after 17 minutes and former Brighton loanee Levi Colwill doubled the lead four minutes later with his first Chelsea goal.
Facundo Buonanotte got one back for the visitors with a superb curling effort and they were right back in the game when Chelsea skipper Conor Gallagher was shown a second yellow card and sent off on the stroke of half-time.
However, Fernandez restored Chelsea’s two-goal advantage from the penalty spot midway through the second half.
Referee Craig Pawson had initially waved play on when James Milner challenged the breaking Mykhailo Mudryk inside the box but awarded the penalty after being sent to the screen by the video assistant referee.
Brighton continued to dominate possession but struggled to create the openings to really worry Chelsea until Joao Pedro pulled one back with a flicked header in the second minute of injury time.
The Seagulls were then given a penalty in the 10th additional minute for a handball by Colwill, only for VAR to intervene again and have the decision overturned as replays showed the ball hit the defender’s head rather than his outstretched arm.
Victory is just Chelsea’s second at home in the Premier League this season, while defeat means Brighton have now won just one of their last eight league games.
Chelsea dig in for important win
There was a minute’s applause before kick-off in memory of former England manager Terry Venables, who also captained Chelsea in his playing days.
Venables’ best sides during his touchline career played with attacking flair, but this victory for Mauricio Pochettino’s men was built on resilience.
The Blues started well and deserved the lead given to them by Fernandez’s close-range header from Benoit Badiashile’s hooked cross.
When Colwill made it 2-0 soon after, it looked like they might run away with it against a Brighton side who were much changed following their Europa League exertions.
However, Chelsea were surprisingly flat following their quickfire double, allowing Brighton a foothold in the match, and they took advantage when Buonanotte received a pass from Adam Lallana, cut it from the right and bent the ball into the far corner.
When Gallagher, who had been booked for a hefty challenge on Buonanotte, then stretched to bring down Billy Gilmour and was sent off, Chelsea fans might have been fearing the sort of collapse they saw at Newcastle eight days previously.
Instead, though, there was a much-needed stubbornness from the home side. They were organised at the back and, for all Brighton’s possession, Chelsea defended stoutly and chances were at a premium.
Joao Pedro’s late goal led to some late drama but Chelsea stood firm enough. The quality in their squad is clear but here they showed the kind of grit that will stand them in good stead going forward.
Brighton fall short at end of memorable week
Coming back from two goals down to take a point, possibly three, at Stamford Bridge would have capped an already historic week for Roberto de Zerbi’s side.
Reaching the Europa League knockout phase with a win at AEK Athens on Thursday was an uplifting but tiring achievement.
Despite their best efforts in this game, it was not to be for the Seagulls.
“I think we played much better than Chelsea,” said Brighton manager De Zerbi.
While Brighton responded admirably to going 2-0 down and enjoyed nearly 80% of possession in the second half, the frustration will be that they lacked the sharpness in the final third to really make it count.
Fatigue may have played a part, but with a busy December ahead and more European football to come in the new year, that is something Brighton will need to get used to.
With so many injuries and suspensions to contend with, even in defeat there was plenty to encourage the Seagulls, and they will focus now on capitalising on home assignments against Brentford and Burnley in the coming days.