Goals from Emmanuel Adebayor and Nicklas Bendtner either side of a strike from Dimitar Berbatov were enough for all the points to take them, temporarily at least, four points clear of Manchester United.
Arsenal were missing Robin van Persie who suffered a recurrence of his knee injury and began the game with the same line-up that started the win over Chelsea, with Alex Hleb playing just behind Adebayor.
Tottenham were without their three first-choice centre-backs and began the game looking nervous.
Arsenal had two good attempts in the first four minutes. Hleb had an over-the-shoulder shot that flew just wide and then Adebayor's edge of the area effort was too close to Paul Robinson.
For most of the next 30 minutes the game saw little goal-mouth action as both sides prodded and pressed in midfield. The game was "tactically locked", as Arsene Wenger tends to describe such periods. The pace was pedestrian, and that suited the visitors.
Robinson was called into action in the 33rd minute when he had to save from Emmanuel Eboue who unleashed a fierce right-foot drive form the right side of the area. The Spurs keeper turned the ball away for a corner that Arsenal subsequently wasted.
Manuel Almunia was involved in the action for the first time on 38 minutes when he got down well to claim Berbatov's free-kick from just outside the Arsenal area.
The Gunners were denied by a fine reflex save from Robinson three minutes before half-time. Kolo Toure rose highest to meet a Cesc Fabregas corner, but the Spurs keeper dived to his left to palm the ball away.
Arsenal had to raise the tempo in the second half and they certainly succeeded in that aim.
Adebayor put the Gunners ahead in the 48th minute following a glorious sweeping move begun by Tomas Rosicky who slipped a ball to Fabregas on the edge of the area.
The Spanish midfielder was aware of Adebayor running into the left side of the area and found the Togolese striker wit ha perfectly weighted and directed back-heeled pass.
Adebayor then picked his spot to fire low past the on-coming Robinson into the right side of the net.
Tottenham were level on 66 minutes through Berbatov who ran on to a clever back-pass from Robbie Keane to shoot through the arms of Almunia from an acute angle from the right side of the area.
The visitors should have scored just seconds earlier, but Keane hit the bar from close range, following some good work by Aaron Lennon and Jamie O'Hara.
Tottenham were awarded a dubious penalty on 71 minutes but justice was done when Almunia dived to his right to save Keane's spot-kick.
However, Wenger then brought on Bendtner for Eboue. The young Dane's first touch was a header into the back of the net from Fabregas' corner to make the final score 2-1 to the hosts.