The unfortunate Wimmer became just the second man after Chris Armstrong to put through his own net in a north London derby during the Premier League era, as Spurs trailed going into the break at Emirates Stadium.
But England international Kane, back in the team after recovering from an ankle injury, struck from the spot early in the second half as Mauricio Pochettino's visitors earned a share of the spoils from an entertaining contest.
The equaliser, Kane's fifth goal in four league meetings with the Gunners, saw the north London derby become the highest scoring fixture in Premier League history.
The result leaves Arsenal third, one point behind leaders Chelsea and three ahead of fifth-placed Spurs.
Tottenham started strongly on enemy territory, Kane narrowly failing to get on the end of an inviting pass to the back post five minutes in after good work down the left from Son Heung-min.
And the striker was inches away from opening the scoring in the 21st minute, his glancing header bouncing narrowly wide from Christian Eriksen's cross.
The Gunners slowly began to assert themselves and, with six minutes to go before half-time, Theo Walcott was found in space down the right and cannoned a vicious strike against the upright with Lloris beaten.
The deadlock was finally broken - through an unexpected source - in the 42nd minute, Wimmer attempting to head clear Mesut Ozil's free-kick only to inadvertently dispatch the ball beyond the reach of the diving Lloris.
Cech was called on to prevent Tottenham from going ahead four minutes later, producing an excellent reaction save to keep out Eriksen's shot after the Arsenal centre-backs failed to clear an awkward high ball.
Jolted into life by those narrow escapes, it was Arsenal's turn to threaten in the 61st minute, Granit Xhaka coming agonisingly close to heading home Iwobi's inviting cross.
Hector Bellerin almost restored Arsenal's lead when he broke into the area with 15 minutes to go, the full-back's deflected shot slipping wide of the post after ricocheting into the body of Kyle Walker.
In the 84th minute, an Eriksen free-kick somehow evaded a host of bodies - including Cech - inside the area, before striking the post and bouncing clear, in what was the last real chance of a game, despite a sustained period of late Arsenal pressure.
The next assignment for Arsene Wenger's men is a trip to face two old enemies in the form of Jose Mourinho and Manchester United after the international break, when Spurs host another capital city clash against West Ham at White Hart Lane.