Chelsea “needed the win” over Brighton, said boss Frank Lampard after his first home victory as a Premier League manager.
The Blues deservedly won to make it nine wins out of nine league games against Brighton – an all-time Premier League/Football League record.
They led at Stamford Bridge when Jorginho scored a penalty after Adam Webster fouled Mason Mount.
Albion, who have not won in the league since the opening day, briefly rallied and Dan Burn’s header hit the crossbar.
But Willian sealed the victory with a deflected strike from Callum Hudson-Odoi’s pass.
Chelsea move up to sixth in the Premier League while Brighton fall to 16th.
“We haven’t had a 90-minute game where we’ve controlled it enough [before now],” Lampard told BBC Sport. “The only disappointment is we didn’t have more goals. We got a clean sheet as well. It is good for the confidence of everyone.
“We had a lot of shots in the first half, but had weak finishing and a bit of bad luck. You do start to wonder but you have to remain confident it will come and it did.”
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The previous record for wins against one team in the league was Wimbledon’s 100% success rate against Bournemouth in eight meetings between 1977 and 1984.
The Blues, with a youthful team following a transfer ban, have been easy on the eye this season but have dropped points regularly.
There had been 25 goals in their opening six league games, but more against than for – and they had not won at home in three top-flight matches.
Lampard had the worst record of any Blues manager this millennium after nine games in all competitions, with no clean sheets.
During the first half, it looked as if they were going to be frustrated with none of their 17 shots going in. Mount went closest when his free-kick from the left wing evaded everyone and hit the post, while Pedro and Tammy Abraham managed five shots each – both had three of them on target without finding the net.
But the Blues kept going and got their reward when Webster fouled Mount, with Jorginho scoring his second goal of the season from the spot.
They dominated for the entire game, bar a short period, and Willian blasted home his first Premier League goal since January, albeit with the help of a deflection.
English youngsters Abraham – the league’s second top scorer with seven goals – Mount and Fikayo Tomori have scored 11 of Chelsea’s 14 Premier League goals, and Lampard was impressed again despite none of them managing to score.
Hudson-Odoi came on for his first Premier League game of the season after recovering from an Achilles problem.
“It is great for the club and a long time coming,” Lampard said. “The work is done in the academy. The mentality is great. They want to play for this club.
“At the moment they are earning it and setting a level for others. I have complete confidence in the lads. They are there on merit. Whatever game, they take it on board and long may it continue.”