The Gunners had stormed into a 3-1 lead after Theo Walcott, Samir Nasri and Robin van Persie all struck in the first half, with Rafael van der Vaart notching for the home side.
But a 20-yard rocket from Tom Huddlestone before the break and a 70th-minute penalty from Van der Vaart ensured that Spurs picked up a point, meaning Arsenal dropped to third, six points behind Manchester United.
Arsenal captain Cesc Fabregas had criticised his team-mates before the match, claiming that the Gunners lacked a killer instinct and that was certainly evident in the second period as they failed to finish their bitter rivals off despite dominating for large parts of the opening half.
Manchester United's draw at Newcastle on Tuesday night meant this encounter was the perfect opportunity for Arsenal to put the pressure back on the leaders and regain some momentum after Sunday's disappointing draw with Liverpool.
Spurs needed little motivation for the match though, as they knew a win would give the club their first league double over their bitter local rivals for 18 years and see them draw them level with fourth-placed Manchester City.
The game started well for Arsene Wenger's men as the game lived up to it's pre-match billing with three goals within the first 12 minutes amid a white-hot atmosphere.
Fabregas took advantage of Huddlestone's carelessness in the centre of the park to release Walcott, who calmly slotted past Spurs goalkeeper Heurelho Gomes from inside the box.
Just two more minutes had passed before Van der Vaart equalised. Vedran Corluka threaded the Dutchman through before he beat Wojciech Szczesny at his near post to claim his first Spurs goal in over two months.
Arsenal were back in the lead five minutes later though as Tottenham's defence were made to pay for backing off as Nasri fired a deflected shot past Gomes from 25 yards.
The match was being fought with genuine steel as Abou Diaby proved when he clattered into Luka Modric, but referee Martin Atkinson waved play on, much to the anger of the home bench.
The Spurs defence seemed to have no answer to Walcott's pace as he raced through their stationary defence on the half-hour only to see his shot trickle wide.
The home fans were given a scare when Gareth Bale was left needing treatment after coming off second-best in an aerial tussle with Szczesny, but he returned to action a couple of minutes later as Tottenham boss Harry Redknapp urged his side to look for an equaliser.
It was Arsenal who got themselves on the scoresheet next though thanks to William Gallas' mistake. The former Arsenal man failed to clear the ball inside the Tottenham box and Walcott crossed to find Van Persie, who beat Gomes at the second attempt after the Brazilian had palmed away the striker's first header.
Bale was carried off on a stretcher after being clattered over by Szczesny and limped throughout the remainder of the half. Two minutes before the break Huddlestone put Spurs back in the game with a wonderfully-hit half-volley from 20 yards after Arsenal had cleared a corner.
Bale did not emerge for the second half and was replaced by Aaron Lennon.
Peter Crouch gave Bacary Sagna a bloody nose as they went up for a header before Wenger brought on Jack Wilshere for Diaby, who hobbled off the pitch through injury.
Spurs started the second half quietly but they suddenly sprang into life in the 54th minute when Modric played in Van der Vaart, who hit a fierce shot that drew a top-class diving save from Szczesny.
Van Persie had the ball in the net soon after but the goal was ruled out for offside, with replays suggesting the Dutchman was half a yard onside.
Walcott broke through for Arsenal again, but this time Benoit Assou-Ekotto tracked back, forcing the England winger to shoot wide.
Spurs were handed a golden chance to get back into the game when Szczesny tripped Lennon in the box in the 70th minute and Van der Vaart duly obliged, slotting home from 12 yards to make it 3-3.
Modric should have put Spurs ahead from six yards but he shot straight at Szczesny, who cleared with his feet on the line.
Wenger, sensing his chances of winning the game, and indeed the title, were slipping away from him, brought on Andrey Arshavin and Nicklas Bendtner for Walcott and Nasri.
Substitute Sandro then danced past two Arsenal defenders before seeing his shot saved by Arsenal's Polish goalkeeper.
Tottenham desperately sought a fourth and Laurent Koscielny almost gifted it to them when his header almost flew into his own net in injury time as a breathless match drew to a close.