Albion overcame bottom-of-the-table Rotherham 2-1 with goals from Tomer Hemed, who netted for the third successive match, and Dale Stephens.
Brighton bossed the first half and took the lead on 27 minutes when Hemed fired home from close range, off the underside of the bar, from Jamie Murphy’s low cross.
Rotherham’s Chris Maguire blazed wide when well placed early in the second half and Brighton doubled their lead on 67 minutes when Stephens drove home from 20 yards.
Slack marking allowed Jonson Clarke-Harris to pull a goal back for the visitors from Joe Newell’s free kick four minutes later but Brighton held on to claim all three points.
Brighton manager Chris Hughton said: “It was a tough night and we had to work very hard to get the second goal. At that stage, the game was in our hands but we made life tough for ourselves by conceding when we did.
“I think that we went through a period in that second half where our game management should have been better; we should have kept the ball.
“However we were worthy winners in the end, based on the performance and two good goals, but no side is going to lay down and die.”
Hughton has been delighted with his side’s start as they sit five points clear of second-placed Middlesbrough and said: “At the moment we are doing enough to win games. We probably have not had the ultimate outstanding performance in a game, but that is this division.
“It is very hard to do that, but at the moment we have enough in us to win games, which is great to see.
“We are delighted to be where we are and the massive thing about being on the run that we are on is that we are accumulating points; and our tally for this stage of the season is brilliant.”
Don’t miss out on all the latest breaking news where you live.
Here are four ways you can be sure you’ll be amongst the first to know what’s going on.
1 Make this website your homepage
2 Like our Facebook page at facebook.com/pages/Sport-Sussex
3 Follow us on Twitter @SportSussex
4 Register with us by clicking on ‘sign in’ (top right corner). You can then receive our daily newsletter AND add your point of view to stories that you read here.
And do share with your family and friends - so they don’t miss out!