Mauricio Pochettino praised the character of his 10-man Chelsea team for battling to a first league win at Stamford Bridge since August.
The Blues led Brighton 2-1 when their captain Conor Gallagher was shown a second yellow card in the 45th minute.
But Chelsea, who had not won a home game in the league since beating Luton, did not crumble as they withstood a late onslaught of Brighton pressure.
Pochettino did not believe Gallagher deserved a second booking but said his side ‘needed’ the challenge of seeing out a win with a man less.