Gabriel Jesus taps in for Arsenal to score in consecutive Premier League home games for the first time since a run of four for Manchester City in November 2020
His side were superior throughout and Spurs' cause was not helped by Emerson Royal's red card for a second-half foul on Gabriel Martinelli.
Arsenal made a fast start and took a deserved lead when Thomas Partey side-footed a precise finish into the top corner from 25 yards after 20 minutes.
Spurs were handed a lifeline before the break when Gabriel's foul on Richarlison gave Harry Kane the opportunity to score his 14th goal in 18 derby games and his 100th goal away from home in the Premier League from the penalty spot.
Arsenal were gifted the lead once again when Spurs keeper Hugo Lloris fumbled badly to allow Gabriel Jesus to score four minutes after the break, Antonio Conte's frustration made worse by Royal's reckless challenge on Martinelli that prompted referee Anthony Taylor to produce a straight red card.
Conte was attempting to make three changes when Granit Xhaka effectively ended the contest with a low finish past Lloris from inside the area.
"We are really hungry, you can feel the desire and the humility, because they haven't done anything yet that's important. That humility is a big driver for us," said Arteta.
"We are focused on what we are doing and today is another sign that we are going in the right direction, that we can play at a really high level."
Arsenal's outstanding start to the season, aided by some smart work in the transfer market in the summer, has raised hopes that they might be coming out of a long period of post-Arsene Wenger transition.
The Gunners were bitterly disappointed to miss out on Champions League football on the final day of last season but there is an energy, verve and threat about Arsenal that suggests they can make a serious impact in this campaign.
Even in defeat at Manchester United last month, Arsenal showed signs of maturity and progress, emphasised here by the manner of their victory over the old rivals.
Arsenal flew out of the blocks to take the lead and even recovered from the frustration of handing an out-of-sorts Spurs a route back into the game via Gabriel's challenge on Richarlison.
Jesus has proved to be a superb signing, while William Saliba has been outstanding in central defence since returning from loan spells at St Etienne, Nice and Marseille.
There is still work to be done but Arsenal look like a club and a team who finally have a clear direction again, a mouth-watering mix of younger players and experience that bodes well for the future.
Arteta now senses that after leading Arsenal to a third successive home win over Tottenham, both his players and the club's supporters are starting to believe they can maintain this success.
"Hopefully it can give the players more belief that they can play at this level and play against any team, doing it in the right way that we want to play," he said.
"We have connected with our supporters and when that happens that's a really powerful thing.
"[The result] is really meaningful because you have the opportunity to give a lot of people happiness and a beautiful day and we have delivered that, so that's really fulfilling."
Arsenal's next game, here against Liverpool next Sunday, will be another significant test but there is growing confidence around Emirates Stadium.
Spurs may argue over the merits of Emerson Royal's red card but it was a poor challenge in a position where he actually had no need to engage with Martinelli. Spurs manager Conte was instantly infuriated by the challenge itself although he was clearly not expecting the punishment that followed.
Conte's side have not been pleasing on the eye this season but they have been digging out results until this first Premier League defeat of the campaign.
Spurs had a spell of threat after Kane's penalty, and indeed the game's first big chance when Arsenal keeper Aaron Ramsdale blocked Richarlison, but they were lacklustre and dominated in all areas.
There was no coming back after the sort of inexplicable mistake Lloris, for all his big reputation, can be guilty of committing, and Royal's red card only pushed any prospect of even a point further into the distance.
Kane and Son Heung-min, who was later substituted along with Richarlison - Conte was trying to make three changes when Xhaka scored Arsenal's third - could not get into the game.
Spurs were well beaten long before the end, Conte cut a resigned figure in his technical area and this was another miserable north London derby away day for manager, player and supporters.
-- Courtesy of BBC Sport