A heavily-rotated Gunners side broke the deadlock in the eighth minute through Reiss Nelson at the Gtech Community Stadium.
And it was an avoidable goal from the Bees' point of view, as Mathias Jorgensen's misplaced back pass was latched onto by Eddie Nketiah.
He then picked out Nelson, who took a touch before coolly slotting the ball home in the bottom right corner from 12 yards out.
Speaking on talkSPORT commentary, ex-Chelsea defender Scott Minto blasted the west Londoners over their gaffe at the back.
He said: "It's a horrendous mistake there in the back five by Brentford.
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"As much as the play that Arsenal have had, they haven't really created any chances.
"The ball fell to Eddie Nketiah, I thought he was going to shoot himself, it was a really bad pass back.
"He reads it well, it looked like for a moment that the ball wasn't going to come and reach Reiss Nelson.
"But he actually showed a lot of composure, he waited for the defender to dive in, the ball came off him, he took a touch and then 12 yards out, he side-foots it past [Mark] Flekken, who had absolutely no chance whatsoever.
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"But that is Brentford just completely gifting the goal to Arsenal."
It turned out to be the only goal of the game - despite Brentford's late onslaught.
Yoane Wissa hit the post, but they were unable to break down a resilient Arsenal side.