The England striker, sidelined since 18 September with an ankle injury, scored from the penalty spot early in the second half after Kevin Wimmer's own goal three minutes before the interval gave Arsenal the advantage.
The Gunners knew victory would put them top of the table, and Theo Walcott almost put them ahead, crashing a shot against the post, before Wimmer glanced Mesut Ozil's free-kick past Hugo Lloris.
Spurs responded well with Kane's spot-kick after Laurent Koscielny tangled with Mousa Dembele. They then threatened to take all three points, Christian Eriksen forcing a fine save from Petr Cech before his angled free-kick bounced back off the post in the closing minutes.
Source: BBC Sports