Since the start of last season, only Liverpool (20) and Manchester City (19) have scored more Premier League goals from corners than Arsenal (17)
Mikel Arteta sent on the schoolboy midfielder in the closing moments with his side leading 3-0.
Arsenal's travelling fans greeted Nwaneri's appearance by singing: "School in the morning, he's got school in the morning."
William Saliba set Arsenal on their way to a sixth win in seven top-flight games this season after the France defender climbed high to head Bukayo Saka's corner in off the post.
It was 2-0 inside the opening half an hour as Brazil forward Gabriel Jesus, a £45m signing from Manchester City in July, headed Granit Xhaka's measured chip past David Raya for his fourth goal in Arsenal colours.
Portuguese midfielder Fabio Vieira capped a dominant Arsenal display by marking his first Premier League start since joining from Porto with a goal from 25 yards.
Brentford were unbeaten in their previous three games and could have climbed to fifth in the table with a win, but they rarely threatened as forward Ivan Toney, who has been called up by England for the first time, struggled for service.
Arsenal had started the weekend top of the table but dropped to third after Manchester City and Tottenham won on Saturday.
This win, however, put the Gunners on 18 points, one more than their nearest rivals before their next match against Spurs in the north London derby at Emirates Stadium on 1 October (12:30 BST).
Arsenal were bullied in the corresponding fixture last season and tamely went down 2-0 against newly promoted Brentford on the opening day of the 2021-22 campaign.
After that game, Brentford striker Toney made a slight dig at the Gunners by tweeting 'nice kick about with the boys', something Arsenal defender Gabriel was quick to revisit after Sunday's win.
A lot has changed since then and this is a very different Gunners team full of grit, determination and character.
After a first setback of the season at Manchester United in their previous Premier League game, all eyes were on how they would respond against a Brentford side that embarrassed United five weeks earlier.
Despite the absence of influential captain Martin Odegaard because of injury, they dominated from start to finish.
Gabriel Martinelli once again put in an eye-catching shift, Saliba was strong at the back while Saka, who also teed-up Vieira, finished with two assists as the Gunners swept to a third clean-sheet away win of the season.
Ben White, left out of the latest England squad, also played a key role while the margin of victory could have been more but for two fine saves by Raya at 3-0 to keep out Jesus and Saka.
Arsenal have not played in the Champions League since 2016-17.
There is still a long way to go, but the signs look promising for Arteta as Arsenal continue to build on a strong start and give their supporters hope they can qualify for European club football's most prestigious competition.
There has been no sign of "second-season syndrome" at Brentford after heavy wins over Manchester United and Leeds.
However, they were distinctly second best against Arsenal yet go into the international break in the top half of the table.
There has been much to celebrate at the club over the past 18 months, not least Toney becoming the first Bees player to be called up by England's senior team since 1939.
Toney went closest to scoring for the hosts following a free-kick but Brentford were below par as they failed to score in the Premier League for the first time since 2 May.
Brentford have come so far in a short space of time but this was a day to forget.
-- Courtesy of BBC Sport