Gareth Bale continued his superb form with the opening goal on 37 minutes and Aaron Lennon made it 2-0 before the interval as Arsenal's defensive deficiencies were ruthlessly exposed.
The Gunners came back strongly after the interval as Per Mertesacker's header got a deflection off Bale on its way to goal, but Tottenham held on to reclaim third place and stretch their lead over Arsene Wenger's men to seven points.
There was a fast tempo to the game from the outset and it was Arsenal who had the first effort on goal when Olivier Giroud's header was comfortably held by Hugo Lloris, while Jan Vertonghen had to be alert to slide in with a good tackle as the French striker threatened again moments later.
Emmanuel Adebayor, sent off against his former club in the reverse fixture at Emirates Stadium, picked up an early yellow card following a reckless tackle on Aaron Ramsey as both sides battled to gain control of a congested midfield.
Arsenal worked their way into a few good positions but were then unable to deliver a decisive final pass, and it was Spurs who suddenly carved out a commanding lead with a two-goal blitz late in the first half.
Bale broke the deadlock with a calm finish past Wojciech Szczesny after beating the offside trap to latch on to a Gylfi Sigurdsson through ball, and it was a similar story two minutes later as Scott Parker's pass set up Lennon to skip round the goalkeeper and double Tottenham's lead.
Arsenal reduced their arrears in the 51st minute when Mertesacker's glancing header from a Theo Walcott free-kick was diverted past Lloris' despairing dive by a touch from Bale.
Nacho Monreal flashed a swerving volley narrowly wide from outside the area and Lloris did well to rush off his line and intercept a dangerous low cross from Carl Jenkinson as Spurs survived a few nervy moments.
Arsenal continued to press forward in pursuit of an equaliser but left gaps at the back for Tottenham to exploit on the counter-attack, although the hosts were not able to capitalise as Bale blazed a glorious chance over the bar and Sigurdsson mistakenly tried to square the ball when he just had the keeper to beat.
Jermain Defoe also drilled an effort wide after coming on for Adebayor and Bale smashed a powerful drive straight at Szczesny, while at the other end Ramsey fizzed a low shot just beyond Lloris' right-hand post from the edge of the area.
Walcott curled a free-kick wide in a frantic finale, and there were six minutes of stoppage time following an injury to Mousa Dembele, but Arsenal could not find a way through as Tottenham clung on to move a step closer to a Champions League spot.