Abdoulaye Doucouré picked up a red card in the second half and with one man more, Tottenham increased the pressure in the only league game of the evening.
It quickly paid dividends.
Michael Keane caused a penalty with a clumsy tackle, Harry Kane stepped forward and won the mental game with Everton goalkeeper, national team-mate Jordan Pickford. Kane waited a long time before placing the penalty in one corner.
Kane has now scored in five straight games – including the European Championship qualifiers with England against Italy and Ukraine.
Tottenham’s Lucas Moura received a red card for a foul tackle on Michael Keane with only minutes remaining and will be banned for a few games.
Keane stood up and in added time he thundered home the equaliser. Thanks to the point, Everton moved up to safe ground at the bottom of the table.
Tottenham is fourth, on 50 points, as many as third-placed Newcastle and fifth-placed Manchester United, but has two more games played than the main competitors for places in the autumn Champions League.
Swedish national team player Dejan Kulusevski played the entire match for Tottenham.