Danny Welbeck scored twice in the first half before Alan Judge made proceedings interesting by scoring a free-kick for the visitors.
Alexandre Lacazette was on hand to put the game beyond doubt for the Gunners by scoring late on as they sealed a sixth consecutive win in all competitions.
Story of the match
Arsenal have had a habit of starting slowly in games this season but they were immediately out of the blocks against Brentford, scoring after just five minutes. Henrikh Mkhitaryan's short corner was played to Matteo Guendouzi and the Frenchman found Welbeck who was free inside the area to head home.
It was a first half dominated by Unai Emery's men as Emile Smith-Rowe almost made it two after being played over the top, but Julian Jeanvier was in his way to prevent a shot on goal.
Arsenal moved the ball about in quick fashion with Alex Iwobi and Mkhitaryan the main creators. They combined after 18 minutes but the Armenian failed to gather the ball properly after getting into the area.
The Gunners' good play was rewarded as they doubled their advantage with 37 minutes gone.
Again Mkhitaryan and Iwobi moved the ball with pace through the midfield, which resulted in the freedom of the left hand side for Nacho Monreal. He laid the ball on a plate for Welbeck who scored his second of the night from close range after a sweeping move.
Moments before that, however, Ollie Watkins could have scored for the Bees. He pounced on Shkodran's Mustafi's giveaway but Rob Holding came across to cover.
The opening 45 minutes suggested that it would be all Arsenal but the Bees had other ideas. Guendouzi gave away a sloppy free-kick on 58 minutes which allowed Judge to step up and curl a wonderful effort over the wall and past Bernd Leno to liven up the tie.
The Emirates had suddenly become a cauldron of noise as Sergi Canos quickly almost found an equaliser, fizzing an effort off target in Brentford's best spell of the match.
It was a period in the game which promoted the introduction of Lacazette who replaced teenager Smith-Rowe shortly after the hour mark.
Brentford's goal could have set up an intriguing final half an hour but the Bees failed to create much more. Instead, Arsenal added a third in injury time. Jeanvier failed to beat Lacazette to the ball and the Frenchman picked up possession before burying his chance clinically.
Takeaways from the game
Welbeck looking sharp:
The England forward raised eyebrows by being selected for the World Cup in Russia but he has started the season in excellent form. Used to playing as a wide player for Arsenal since he signed for the club, Emery decided to field him as the side's main striker against Brentford.
It was a decision that paid dividends as he scored a fine header before capping off a classic Gunners counter attack to add a second goal.
Iwobi a direct presence:
Under Arsene Wenger, Iwobi often cut a frustrated figure. However, since Emery took over he looks to be back to his best.
He put in another promising attacking display against Brentford, following on from a good performance against Vorskla in the Europa League. He had the goal in the back of the net in injury time but unfortunately for the Nigerian it was ruled out for offside.
Brentford can mix it with Premier League's best:
Dean Smith's team finished last season by just missing out on the Championship play-offs finishing in ninth place. This season they currently sit in seventh and look a side capable of achieving promotion.
Therefore a test against one of the best team's in the country was an intriguing proposition for them. Their first half display wasn't overly convincing but they took the game to the Gunners in the second half and showed they were capable of producing quality against a Premier League side. Perhaps we'll see more of it next season.
Stand out players
It wasn't a game filled with too much outstanding quality but Welbeck will be at the front of the queue for the man of the match award. He didn't touch the ball on too many occasions but when he did it mattered greatly as he notched his third and fourth strikes of the season.
For Brentford, Watkins was lively and tested Mustafi who at one point was left on his backside by the forward. Canos was another who looked direct and caused problems for the Gunners backline throughout the second half. Ultimately it wasn't enough for the Championship outfit as they exited the competition.