The Bees boss made two changes to the side that started the previous Premier League game against Bournemouth .
Michael Kayode replaced Aaron Hickey at right-back, while Mikkel Damsgaard came into midfield in place of Mamadou Sangaré.
Former Bee Jordan Henderson started for the visitors.
The first chance fell Chelsea's way on nine minutes. Keane Lewis-Potter was unable to clear Pep Chavarría's deep cross from the left, allowing Danny Welbeck to bring the ball under control and lay it off for Pedro Neto . The winger's first-time strike was palmed away by Caoimhín Kelleher .
Morgan Rogers seized the loose ball and drove towards goal but scuffed his shot.
Midway through the first half, Michael Kayode's long throw bounced through to Lewis-Potter, whose volley was blocked by Cole Palmer .
After Damsgaard conceded a free-kick on the edge of his own box, Rogers got the ball up and over the wall, although his attempt lacked power and was comfortably held by Kelleher.
Damsgaard sent the ball down the channel in search of Thiago. The striker held it up brilliantly under pressure from Levi Colwill and picked out the advancing Yehor Yarmoliuk . The midfielder's low drive from distance was dealt with by Martínez.
Lewis-Potter then cut inside and played a short pass to Damsgaard, who fired over the crossbar from 20 yards.
Chavarría motored down the left and cut the ball back for Rogers, only for Schuster to block his goalbound strike.
After Janelt 's attempt was blocked, Thiago teed up Lewis-Potter, who fired straight at Martínez.
In the first action after the break, Kevin Schade found Thiago, who moved the ball on to Yarmoliuk. Anthony met the Ukrainian's cross and headed against the crossbar, although the assistant's flag was raised for offside.
Damsgaard and Janelt combined deep inside Chelsea territory, with the former sending a beautiful low cross with the outside of his boot narrowly beyond Anthony in the six-yard box.
Damsgaard produced a clever turn to escape his marker and lifted the ball towards Schade on the shoulder of the last defender. Fofana won the aerial battle and headed clear, before Thiago met the bouncing ball first time and sent it over the crossbar.
Neto then broke down the left and took aim from a tight angle, only to fire over.
Brentford made the breakthrough on 61 minutes with a well-executed set-piece routine. Damsgaard whipped a corner to the back post, where Schuster nodded the ball back across goal for Anthony to head in his first Brentford goal from close range.
Chelsea went close on 68 minutes. Schuster made first contact with an in-swinging corner, although Colwill was unable to react quickly enough to turn the loose ball towards goal.
Palmer spun away from Mamadou Sangaré inside a crowded penalty area, with his strike taking a deflection and going behind for a corner.
Brentford doubled their advantage on 80 minutes. Damsgaard released Schade beyond the Chelsea backline and, after the forward's attempt was kept out by Martínez, Thiago stole in to convert the rebound and open his account for the Premier League campaign.
The striker raced towards the corner, whipped off his shirt in celebration and then embraced Andrews,who had sung his praises during Thursday's pre-match press conference.
Carvalho put the gloss on an impressive victory in the final seconds. Schade's low cross from the left took a slight nick off Josh Acheampong and ran through to the substitute, who timed his arrival at the back post to perfection before converting from close range.
The victory extended Brentford's unbeaten Premier League run at Gtech Community Stadium to eight matches, stretching back to February.
Brentford (4-3-3):Kelleher; Kayode (Hickey 69), Ajer , Schuster, Lewis-Potter (Diouf 81); Janelt, Yarmoliuk (Sangaré 69), Damsgaard (Carvalho 87); Anthony ( Ouattara 81), Thiago, Schade
Subs not used:Balcombe, Henry, Wilson, Fredrick
Chelsea (3-4-2-1):Martínez; Fofana (Acheampong 71), Lacroix, Colwill; Neto ( Estêvão 87), Henderson, Barco (Nicoll-Jazuli 87), Chavarría; Palmer, Rogers; Welbeck ( Quenda 71)
Subs not used:Penders, Gusto , Hato , Lavia , Gittens
Attendance:17,193
Head coach Keith Andrews was full of pride after watching his side secure an emphatic west London derby victory.
"I feel like I've played – I feel like I've kicked every ball," he said.
"I really enjoyed us tonight. We had to show different attributes: grit, resilience, passion and enthusiasm.
"We had a positive mindset to take the game to them and scored in different ways. We defended resiliently again.
"I just loved us tonight. I loved everything about it."
Jaidon Anthony was delighted with Brentford's second-half display and described scoring his first goal for the club as an "unbelievable feeling".
"I'm really happy," he said. "Especially in the second half, I thought we were unbelievable. We really got after them. 3-0, we couldn't ask for much more.
"[Andrews] instils a lot of belief in us through how we work and operate. At half-time, he just wanted us to increase the intensity and keep believing. I thought we did that.
"I don't score too many headers! Fab [Carvalho] told me a couple of days ago that I was going to score, so I'm really happy with that one. It was an unbelievable feeling."
