PHOTO: AFP
Aaron Ramsey's first-half goal put Arsene Wenger's side ahead, but the dismissal of Arsenal midfielder Francis Coquelin in the 55th minute shifted the game in Spurs' favour, with Toby Alderweireld and Harry Kane putting the hosts ahead.
However, the visitors showed impressive determination to recover through Sanchez's 76th-minute effort to revive their faltering title challenge.
It was leaders Leicester City who were the main beneficiaries, though, with Spurs now two points behind Claudio Ranieri's side, who face Watford later on Saturday, while the draw left Arsenal five points off the top.
Advantage Leicester as Spurs, Arsenal, Manchester City lose
Wenger acknowledged the importance attached to this game when he admitted beforehand, it was one of the most significant north London derbies he has been involved in.
And while the outcome was vital to both teams, there was little doubt Arsenal came into the clash facing more questions about their ability to sustain their title challenge.
The midweek home loss to Swansea City, coming on the back of the disappointing defeat at Manchester United, had drawn criticism of Wenger and his players, but their fightback with 10 men at least temporarily answered the doubters.
Wenger reacted to the Swansea loss by making four changes to his starting line-up, with David Ospina replacing the injured Petr Cech in goal and Kieran Gibbs coming in for Nacho Monreal at left-back.
Lacking fight: Sanchez challenges Arsenal to show title desire
In midfield, the manager introduced Mohamed Elneny for his first Premier League start, while Wenger's frustrations at his side's recent efforts up front prompted his decision to start with Danny Welbeck.
Tottenham had also gone into the game on the back of a defeat -- the 1-0 loss at West Ham United that prevented them moving to the head of the table -- but there had been no suggestion of a growing crisis at White Hart Lane.
And with Mousa Dembele and Dele Alli restored to the starting line-up after injury, the home side started with more confidence, quickly taking control of the game.
Arsenal had offered little as an attacking force but still managed to force the lead with their first meaningful attempt on goal in the 39th minute.
Welbeck benefited from a fortunate deflection that freed him down the left, but the forward showed great awareness to delay his cross before picking out the run of Hector Bellerin.
The right-back's pass towards the centre of goal found Ramsey and the Wales midfielder was on hand to direct the ball past Hugo Lloris with a clever back-heel.
Wenger's men should have found themselves two up moments later when Welbeck directed a header too close to Lloris from Sanchez's cross.
Spurs were stunned at finding themselves behind, but were given a helping hand in their efforts to get back into the game when French midfielder Coquelin collected a second yellow card for an ill-judged sliding tackle on Kane after being booked for handball in the first half.
The dismissal was always likely to prove costly and within five minutes Tottenham were level when Alderweireld finished from close range following a corner.
Spurs were on a high and their renewed confidence was illustrated by Kane's spectacular effort that put them ahead just two minutes later.
Alli worked hard to keep the ball from going out for a goal-kick before Kane picked up possession near the by-line and curled a 20-yard shot beyond Ospina from a tight angle.
Arsenal's cause seemed lost, but to their credit, they continued to pursue an equaliser despite being a man down.
It came in the 76th minute when Sanchez moved to collect Bellerin's pass and send a shot across Lloris and inside the far post.
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