Aaron Ramsey gave the Gunners the lead on 38 minutes by flicking Hector Bellerin's low cross beyond Hugo Lloris in the Tottenham goal.
But the tables turned when Arsenal midfielder Francis Coquelin was shown a second yellow card shortly after halftime for a needless foul on Spurs striker Harry Kane.
Within minutes, Toby Alderweireld had leveled for the hosts from close range. Kane then put Spurs in front shortly after with a curling shot from a seemingly impossible angle.
Yet Arsenal battled on despite its numerical disadvantage and drew level when Alexis Sanchez fired low beyond Lloris when slipped through on goal by Bellerin.
Arsenal's second choice goalkeeper, David Ospina, also played his part stepping in for the injured Petr Cech to secure the result.
The Colombian made nine saves throughout the match to keep Spurs forward line at bay -- a stat that frustrated Spurs striker Kane.
"We are disappointed, it's an opportunity missed," Kane told BT Sport after the match. "We should have got the third and fourth and that would have been the end but if you give top sides room they punish you."
The result means Tottenham remains second in the EPL table, three points ahead of Arsenal in third place with just nine games of the season remaining.
As such, the real victors from all the drama in north London could be league-leaders Leicester City, which can stretch its current two-point lead atop the table with a win away to Watford later Saturday.
"If Leicester win at Watford, they are in a very good position and they don't depend on other people's results," Arsenal boss Arsene Wenger later told reporters.
Asked whether Arsenal can still win the league despite damaging recent defeats to Manchester United and Swansea, Wenger added: "I don't know. Let's see what happens over the weekend but we have to take encouragement from today and if we can reproduce that we still have a chance."
"It shows that we had the right spirit and balance in the team, and overall we had a solid performance," Wenger added.