Enzo Fernandez put Chelsea in front with his first Premier League goal of the season
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.
-- Courtesy of BBC Sport