Ben Chilwell kept up his scoring streak but gave all the credit to Edouard Mendy after the Chelsea goalkeeper defied Brentford with a string of vital saves, securing a valuable three points.
Chelsea's 1-0 win against their west London rivals came thanks to Chilwell's fine strike in the 45th minute, his third goal in his past three games.
Mendy produced six saves to preserve what Chelsea boss Thomas Tuchel described as "not the cleanest sheet we ever had".
The shutout was Mendy's 20th in the Premier League from just 38 starts. In the competition's history, only Petr Cech (26), Pepe Reina (32), Alisson (36) and Roy Carroll (37) have needed fewer starts to reach 20 clean sheets, Opta said.
"It was pretty much Hell on Earth for the last 20 minutes but we did well," Chilwell said.
"I think we've got Edou to thank. In the last 25 minutes he was superb. He's amazing. We see it every day in training, but he's getting the credit he deserves in these sorts of games where he makes the big saves and gets us the three points in the end."
Using Opta's expected goals on target model, Mendy can be shown to have prevented 3.5 goals this season, more than any other keeper in the Premier League.
Chelsea lead the way in the Premier League with 19 points from eight games, just the start they were seeking as they attempt to follow up last season's Champions League triumph with a strong domestic campaign.
Chilwell, back in favour and showing his value with two goals for Chelsea either side of a maiden strike for England against Andorra, said: "I'm happy to get on the scoresheet. Defensively it was tough today, but we showed our steel and showed how strong we are defensively."
Tuchel told Sky Sports that Chelsea could have managed the last quarter of the game in a better way, rather than allowing Brentford to dictate the tempo.
Brentford's Bryan Mbeumo hit the post twice in the match. He has now been denied by the frame of the goal six times in the Premier League this season – more than any club in the competition.
"In the end, the last 20 minutes, it was suddenly a cup game. They had nothing to lose and they felt the belief and felt the momentum with the crowd," Tuchel said.
"Suddenly it seemed like we had one player less on the field. They brought six or seven guys into the box constantly. We were not clear enough in the challenges. They played with the energy like in a cup game. We focused too much on defending.
"I was very, very happy with the first 65 or 70 minutes. We should have maybe scored one more but it can happen – respect to Brentford in the end.
"It was not the cleanest sheet we ever had but very, very important to get the three points, so it was up to Edou."
Tuchel is not reading much into his team's lofty standing in the league table, given Liverpool and Manchester City are in close pursuit.
He said: "It's better to be there than the other way round. But it's too early, and there are way too many teams that are close, so with every draw and every loss you can lose three or four positions, so it's not the main point now in October.
"It was a late win but a deserved win today. We needed a bit of luck in the last 20 minutes but I'm happy with the energy – I can recognise us and I'm happy with the way we play."