Kane's spot kick was enough to secure Spurs' first draw of the Premier League season but only after high drama in injury time, when Pierre-Emerick Aubameyang saw a spot kick of his own saved.
Referee Anthony Taylor was at the centre of the controversy, awarding an offside Kane a penalty to level before pointing to the spot when Davinson Sanchez appeared to foul Aubameyang in the area, much to Tottenham's fury.
But Hugo Lloris guessed right and brilliantly denied Aubameyang before Jan Vertonghen somehow diverted the rebound over the bar. There was still time for Lucas Torreira to see red in an absorbing derby for a foul on Danny Rose.
The result keeps Tottenham four points clear of their north London rivals in the race for the top four, ending a run of back to back defeats.
Ramsey had opened the scoring on 16 minutes after Sanchez had failed to deal with a header and was muscled off the ball by Alexandre Lacazette, who played the ball into his teammate's path. The Wales international had the freedom of the Tottenham half and kept his composure well to finish past Lloris, who had remained rooted on his line.
However, Kane's 74th minute penalty ensured the spoils were shared.
Kane thought he had pulled the hosts level just moments after Ramsey's opener when he powered home a header from Eriksen's free-kick but was correctly ruled offside before Arsenal goalkeeper Bernd Leno produced a sensational double save just before half-time.
Kane was offside again in the second half but the officials missed it and he was bundled over by Shkodran Mustafi before stepping up to level. Arsenal had a glorious chance to win it in injury time before Lloris made himself a hero and Unai Emery's men then had to see out the closing stages with 10 men after Torreira clattered Rose.
Tottenham's first draw of the campaign means they could find themselves 11 points behind Liverpool should the league leaders win Sunday's Merseyside derby.
Arsenal, meanwhile, will drop to fifth place should Manchester United beat Southampton on Saturday, while they have still not kept an away clean sheet all season and have won just once on the road since Nov. 25.