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 in securing the result.
The Colombian, who was deputizing for the injured Petr Cech, 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 was league-leader Leicester City, which stretched its lead atop the table with a 1-0 win away to Watford later Saturday.
Riyad Mahrez scored the only goal of the game for the Foxes at Vicarage Road with a perfectly placed curling strike from the edge of the Watford area early in the second half.
Speaking to reporters shortly after his own side's match, Arsenal boss Arsene Wenger admitted that "if Leicester win at Watford, they are in a very good position and they don't depend on other people's results."
When asked whether Arsenal can still win the league after securing a battling draw at White Hart Lane, 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.
West Ham comeback, Man City return to winning ways
Elsewhere in the EPL Saturday, West Ham came back from two goals down to defeat Everton 3-2 with talismanic midfielder Dmitri Payet scoring the winner in injury time.
Manchester City returned to winning EPL ways with a comfortable 4-0 win over basement boys Aston Villa. Sergio Aguero bagged a brace then missed a penalty City. Yaya Toure and Raheem Sterling were also on target for the light blues.
At the bottom of the table, Norwich City's miserable run continued as it went down 1-0 at fellow strugglers Swansea.
Newcastle United was eased aside 3-1 at St James' Park by Bournemouth while a last minute goal by Virgil Van Dijk rescued a point for Southampton at home to Sunderland.
Chelsea maintained its long unbeaten Premier League run under Guus Hiddink but was left frustrated in a 1-1 draw at home to Stoke City.