Frank Lampard was relieved to get a first Premier League home win as Chelsea boss under his belt after second-half goals from Jorginho and Willian sank Brighton 2-0.
The Blues had peppered the Brighton goal throughout the first half but only made the breakthrough when Jorginho tucked in a penalty five minutes after half-time.
Willian's well-taken second secured a maiden three points at home for Lampard, while Brighton never really threatened to deny the hosts a first clean sheet of the season.
"We've been waiting for that," said Lampard. "The home games have been frustrating. You could almost feel the frustration at half-time because we hadn't scored.
"What pleased me was the performance. The message at half-time was to not get despondent and keep playing at pace.
"When you're not winning at home you fear the worst, but it felt different today.
"I felt it was coming and it was important to say that to the players. They deserved something to drop and it came with the penalty."
Premier League highlights & review: Wins for Liverpool, Manchester City, Chelsea, Tottenham and Wolves
Chelsea had 17 shots - three of them sitters - in a one-sided first half.
They were inches away from taking the lead when Tammy Abraham glanced a header which bounced against a post.
Ross Barkley should have put the Blues ahead in the 36th minute when he met Marcos Alonso's cross at the far post but his cushioned volley gave Mat Ryan the chance to save.
Worse was to come in front of the Brighton goal, Pedro shooting straight at Ryan when clean through before Alonso arrived at the far post only to blaze over from three yards out.
Brighton somehow survived the first half, but five minutes into the second Adam Webster hit the self-destruct button.
The defender's poor touch in the area allowed Mason Mount to poke the ball away from him and as Webster tried to win it back he tripped the youngster.
Jorginho assumed penalty-taking duties despite Pedro notching one against Grimsby in midweek and the Italian coolly rolled it home.
Brighton briefly threatened an equaliser, Steven Alzate seeing a shot deflected wide before Dan Burn headed the resulting corner into the ground and up off the crossbar.
But their rally was short lived, Callum Hudson-Odoi feeding Willian who charged into the box and finished at the near post.
For the Seagulls, the Graham Potter revolution has yet to take off and they have now not won since the opening weekend of the season.
"We were stubborn and put up a fight but we were lucky to go in at 0-0 to be honest," said Potter.
"There was nothing wrong with the effort, the boys gave everything and you have to give credit to the opposition. Chelsea were good.
"Adam's got tremendous quality with the ball at his feet but mistakes happen.
"We grew into the game a bit, hit the bar and had a chance to get a foothold but then the second goal killed us off a bit.
"Overall Chelsea deserved to win. We have to improve. That's our challenge."
