After heading the Gunners in front after four minutes, Welbeck rounded off a fine team move for the second before the interval.
The Gunners have won their last four games in the Premier League to bounce back from a hard start to the 2018-19 season.
Danny Welbeck opened the scoring for the Gunners in the fifth minute with a header inside the box following a quick and clever shot-corner. Brentford attacker Alan Judge would pull one back for the visitors in the 58th minute with a superb free-kick, although in-form frontman Alexandre Lacazette came off the bench to score a third goal in stoppage time to seal the win for Unai Emery's side.
Emery said he was "very happy" with Welbeck when asked if he wanted the attacker to remain beyond the current campaign and praised the pressure he is applying to the established duo. Danny Welbeck is working with this commitment and when he is playing also with a performance like today, and I think he's helping the team and we want this. Meanwhile, Mesut Ozil and Pierre-Emerick Aubameyang have been rested completely by Emery.
Man Utd boss Mourinho knews cameras were watching for Pogba clash
Speaking on Sky Sports he added: "No fallout at all, no problem at all, just a decision that I don't have to explain". The two players remain on good terms but club insiders have noticed they are not as close as before.
'I want to look at him also with our best performance and for him to stay in first XI'.
"I know they are in the previous year and are speaking with the club".
For Brentford, they return to their Sky Bet Championship promotion bid with manager Dean Smith making seven changes.
Emery delighted in the victory post-match, while also saluting Welbeck, who played a key role in the win. "We forced a very good team into mistakes and nearly took them to penalties at the end".