- Ben Chilwell (45')
Ben Chilwell's stunning first half strike turned out to be the winning goal as Thomas Tuchel's team survived a late rally from the newly-promoted side.
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Chelsea needed Edouard Mendy to produce a number of important saves in the second half to come away with the three points.
Chelsea are now a point ahead of second-placed Liverpool while Brentford stay in seventh position.
"We were very strong for 70 minutes and very lucky for 20 minutes, to sum it up. We escaped with the three points thanks to Edouard," Tuchel told BBC.
"It was like a cup game at the end; they took risks and the atmosphere gave them a lot of courage."
After a slow start, the game came to life after 23 minutes when Brentford came close to taking the lead but Bryan Mbeumo's close-range strike hit the post.
Following the chance, Chelsea went up the other end and Romelu Lukaku put the ball in the back of the net but it was ruled out for offside.
Timo Werner should have opened the scoring after 37 minutes but fired his shot over the bar from inside the box.
The visitors did take the lead on the stroke of half time when the ball bounced to Chilwell who struck a stunning half volley into the top corner.
After the break, Brentford enjoyed the better chances with Ivan Toney forcing a good save from goalkeeper Mendy while Mbeumo struck the post for the second time.
Mendy pulled off another stunning fingertip save from Christian Norgaard's volley in stoppage time as Chelsea claimed a vital victory.
"It is difficult to believe we dominated Chelsea, particularly in the last 30 minutes, and they are very lucky," Brentford coach Thomas Frank told BBC.
"That is crazy. Four months ago, they won the Champions League and we got promoted through the play-offs. They dominated without creating anything in the first hour, and after we made changes we created chances.
"We kept them to five shots, five shots, I'm talking about Chelsea. That is impressive. I can't ask for more; if we play this game 10 times, we win nine."
|Brighton & Hove Albion||14||6||4||4||+4||22|
|West Ham United||14||6||3||5||0||21|