Mikel Arteta's side made it seven wins from eight league games this season as they moved four points clear at the top of the table.
The 192nd meeting between these bitter rivals from opposite ends of the Seven Sisters Road was a typically frenetic occasion from the moment Thomas Partey put Arsenal ahead early in the first half.
Harry Kane equalised with a penalty but third-placed Tottenham imploded after the interval as Hugo Lloris's mistake allowed Gabriel Jesus to restore Arsenal's lead.
Tottenham defender Emerson Royal was sent off for an ugly foul on Gabriel Martinelli before Granit Xhaka's goal ensured Arsenal would avenge the 3-0 defeat against their hated neighbours last season that cost them a Champions League place.
Ending Tottenham's 13-match unbeaten run in the league was a significant statement of intent from Arsenal.
Arsenal have now lost just once in 30 home league games against Tottenham, yet there was far more than local bragging rights at stake for the Gunners.
Their only previous match against a top-four rival this season ended in a 3-1 defeat at Manchester United, but this dynamic performance showed they must be taken seriously in the title race.
Next Sunday's showdown with Liverpool will be another test for Arsenal, but while champions Manchester City remain the title favourites, Arteta's team are emerging as a force to be reckoned with.
Arsenal quickly seized the initiative, penning Tottenham back into their own penalty area before Martinelli met Bukayo Saka's cross with a fierce strike that Lloris pushed onto the post.
Despite their vibrant opening, Arsenal were fortunate not to fall behind when Son Heung-min's cross reached Richarlison, who should have done better than poke tamely wide from six yards.
But with Tottenham sitting too deep in a desperate bid to soak up Arsenal's pressure, the Gunners took the lead in stunning style after 20 minutes.