Mauricio Pochettino was able to recall Mousa Dembele following a groin injury and the Belgium international lined-up against an Arsenal midfield in which Mohamed Elneny made a first Premier League start.
Kane had a rising sixth-minute effort deflected behind as Tottenham got themselves on the front foot amid a frenetic opening.
Much of the pre-match build-up focused on Petr Cech’s injury absence but his deputy in the Arsenal goal, David Ospina, reacted superbly when Erik Lamela turned Kyle Walker’s angled shot goalwards in the 26th minute.
Danny Welbeck, preferred to lead the Arsenal attack ahead of Olivier Giroud, cut an isolated figure as Tottenham made much of the first-half running, although the England man played a key role as Arsenal opened the scoring.
Leading a counter attack down the left, Welbeck played the ball across the area for on-rushing full-back Hector Bellerin, whose cutback was wonderfully backheeled home by Ramsey.
Tottenham’s earlier poise appeared to desert them completely and, with Sanchez making an increasing menace of himself, Welbeck wasted a headed chance to increase the visitors’ advantage.
Early in the second half, Walker was allowed to advance and test Ospina with a stinging drive, although Arsenal remained relatively comfortable until Coquelin erred decisively in the 55th minute.
The French midfielder, booked earlier for a robust tackle on Eric Dier, slid in rashly as Kane advanced down the left to leave referee Michael Oliver with little choice.
Seven minutes on from the red card Arsenal found themselves behind. Having required a brave stop from Ospina to deny Kane from Alderweireld’s flick on, Wenger’s men left the defender unmarked to slam home from Lamela’s 60th minute corner.
With White Hart Lane still rocking from the equaliser, Dele Alli – amid suspicions of offside – hustled Per Mertesacker out of possession to backheel to Kane.
The England striker still had much to do but magnificently curled home his 20th goal of the season in all competitions from a tight angle, the ball clipping the inside of Ospina’s far post before nestling in the net
Ospina blocked a Dier shot as Tottenham briefly threatened to run riot, although Pochettino’s pragmatic decision to sit on the lead would let Arsenal back in to earn a share of the spoils.
If Wenger sending on Giroud in place of Elneny carried an air of desperation, there was nothing but cold precision from Sanchez as he latched on to Bellerin’s pass to steer the equaliser across Lloris.
Wenger was understandably furious as Oliver failed to show Dier a second yellow for pulling Giroud back and, despite an acrobatic stop from Ospina to deny Christian Eriksen, Arsenal carried the greater threat in a thrilling finale.
That almost resulted in a winning goal for the Gunners but Ramsey was denied in injury-time by a wonderful, last-ditch tackle from Kevin Wimmer.