The Portuguese midfielder curled in Arsenal's third goal with a long-range effort via the post in the 49th minute after starting in place of the injured Martin Odegaard.
Defender William Saliba and Gabriel Jesus both scored with headers in the first half as the Gunners cruised to a comfortable victory in a stadium where they lost 2-0 last year in the season opener.
Arsenal manager Mikel Arteta even had the luxury of sending on 15-year-old Ethan Nwaneri for the last few minutes, making him the youngest player ever to appear in a Premier League game.
The win gives Arsenal 18 points from seven games, one point ahead of Manchester City and Tottenham going into the international break. The Gunners next face Tottenham at home in the north London derby on Oct. 1.
Brentford was coming off a 5-2 home win over Leeds and also beat Manchester United 4-0 at the Gtech Community Stadium but barely had a sight of goal against a solid Arsenal defense. Striker Ivan Toney — who was given his first England call-up this week — shot over the bar from a free kick in the 53rd but was otherwise kept quiet.
Arsenal goalkeeper Aaron Ramsdale didn't have a save to make until he stopped substitute Mikkel Damsgaard's low shot in the 71st — while the crowd was on its feet for a minute's applause to mark the 70-year reign of Queen Elizabeth II, whose funeral will be held Monday.
As with all Premier League games this weekend, the queen's death was marked with a minute's silence before kickoff followed by a rendition of the national anthem.
Arsenal took the lead when Bukayo Saka swung in a corner from the right that was met by Saliba, whose looping header went in off the far post.
Jesus then netted his fourth league goal of the season in the 28th by heading in a perfect delivery from Granit Xhaka, who dictated play in midfield throughout the game for Arsenal.
And Vieira took away any hopes of a Brentford comeback when he collected a pass from Saka and unleashed a 30-yard curler with his left foot past diving goalkeeper David Raya.
Saka nearly netted a fourth in the 66th when he drew a one-handed save from Raya with another long-distance effort. Raya also denied Jesus a second goal in the 87th, getting down low to palm away the Brazilian's shot from a tight angle.
Nwaneri came on in injury time to break the Premier League age record previously held by Harvey Elliot, who was 16 years and 30 days when he made his first appearance for Fulham — leading to chants of “he's got school in the morning” from the away fans.