An eventful first half saw Fernandez and Levi Colwill find the net in the space of four minutes to give the hosts a two-goal cushion.
Despite establishing an early advantage, Chelsea's task became much tougher when Facundo Buonanotte pulled a goal back before Conor Gallagher was shown a red card in the closing stages of the first period.
Although the Blues were left a man light, Fernandez added his second and Chelsea's third in the 65th minute, dispatching his spot kick after James Milner had been penalised.
Joao Pedro pulled a goal back in stoppage time, and while Brighton briefly thought they had a late penalty, a quick review showed no handball infringement had occurred, ensuring that the Seagulls fell to a narrow defeat – a result which ends their seven-game unbeaten run in all competitions.
Chelsea, who are celebrating their first home league win since August, move up to 10th position and to within three points of the eighth-placed Seagulls.
Chelsea came into the contest looking for a response after suffering a heavy 4-1 defeat to Newcastle United last weekend.
The Blues certainly made a positive start to proceedings, establishing a two-goal lead inside the opening 21 minutes.
Fernandez got the hosts up and running when he headed home from Benoit Badiashile's hooked ball into the danger zone.
Former Brighton loanee Colwill quickly doubled Chelsea's advantage, nodding in after Nicolas Jackson had headed the ball back across goal.
Instead, it was the Seagulls who celebrated the next goal through Buonanotte, who neatly cut onto his left foot and thumped the ball beyond the outstretched ex-Brighton goalkeeper Robert Sanchez.
The South-coast side received another boost on the stroke of half time as Chelsea midfielder Gallagher was given his marching orders for two bookable offences.
After negotiating the opening 20 minutes of the second period, the hosts were given the chance to restore their two-goal advantage when Milner was penalised for bringing down Mudryk following a VAR review.
With usual penalty-taker Cole Palmer still waiting to come on, Fernandez shouldered responsibility and kept his composure to fire down the middle of Steele's goal.
Brighton searched desperately for a way back into the contest, and their quest bore fruit in stoppage time courtesy of Pedro's flicked header from Milner's near-post corner.
There was to be one final moment of drama as referee Craig Pawson ruled that Colwill had handled the ball in the penalty area, only for VAR to show that it had struck him in the face instead.
After ending a five-game winless home league run, Chelsea will now prepare for Wednesday's meeting with Manchester United at Old Trafford, while Brighton welcome Brentford to the Amex Stadium.No Data Analysis info