The Blues hit eight past Grimsby in the Carabao Cup in midweek but were largely wasteful and despite registering a total of 24 shots, they had to wait until the 76th-minute to seal the points when Willian's deflected shot slipped past Matt Ryan.
Brighton didn't have a shot of any kind until the hour mark, Dan Burns spurning a wonderful opportunity to equalise just before Chelsea's second when he headed onto the post from Pascal Gross' corner delivery.
It was a day of firsts for Chelsea as they finally registered a clean sheet in the league and with it, move up to sixth in the table. They travel to Lille on Wednesday night in the Champions League next, while Brighton drop a place to 16th and host Tottenham Saturday next in the Premier League.
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Chelsea's youngsters shine: They started the game in 11th place but their current league position of sixth is a more accurate reflection on their season so far. This is a young side brimming with enthusiasm, pace and raw ability. They have a lot to learn but the supporters are going to enjoy the ride. After countless short-term managers, perhaps the Blues have finally found their gem. You could see how much this victory meant to Lampard at the final whistle.
MAN OF THE MATCH
Mason Mount (Chelsea): The 20-year-old was a real livewire throughout, constantly popping up in space and driving his team forward with rapid pace and vigour. Fikayo Tomori was excellent in defence and Callum Hudson-Odoi made a real impression coming off the bench for his first appearance since April. These are exciting times at Stamford Bridge.
Chelsea: Kepa 6, Azpilicueta 7, Christensen 6, Tomori 8, Alonso 6, Jorginho 7, Barkley 6, Mount 9, Willian 7, Abraham 6, Pedro 6. Subs: Kovacic 5, Hudson-Odoi 8, Batshuayi N/A.
14' - POST! How did that not go in? Mount swings a free-kick in from the left, Abraham doesn't make the connection with his header and the delivery ends up smacking the post!
41' - ANOTHER MISS! Azpilicueta lifts a deep cross from the right, Alonso is unmarked and ought to score, but he slips and sends the ball high into the stands.
50' - GOAL! Chelsea 1-0 Brighton. Jorginho slides the ball bottom left for his first league goal of the season. Ryan didn't move.
73' - WOODWORK! Brighton should be level! Burns slips away from his marker to meet the corner delivery, his header bounces off the surface, off the crossbar and over the bar.
76' - GOAL! Chelsea 2-0 Brighton. Willian puts the game out of sight with a well-taken goal. Hudson-Odoi is the creator with his rapid pace, running 40 yards before switching it to the Brazilian. He powers a shot, it takes a deflection off Burns and slips past Ryan.
Willian scored his first goal in 17 Premier League appearances for Chelsea since he last found the net against Newcastle in January; he had attempted 32 shots without scoring between these goals in the league.
Jorginho's penalty is the 100th to be scored at Stamford Bridge in the Premier League (78 for Chelsea, 22 against), making it the first ground to reach this milestone in the competition.
Chelsea have now won all nine of their league meetings with Brighton, making it a new Football League record for most games played by a side against a single opponent while winning every single one, overtaking Bournemouth’s eight games against Wimbledon.