Spurs opened up the scoring in north London with Eric Dier managing to lash the ball home from close range, after the Everton defence failed to deal with a corner.
The hosts had the lead at the break but Theo Walcott scored an equaliser on 69 minutes, before the Toffees went ahead for the first time three minutes later thanks to Cenk Tosun.
That lead only lasted a further three minutes, as Christian Eriksen produced a fine strike to level the score once more on 75 minutes.
The Danish international, who has been linked with a move away from Spurs this summer, lined up a perfectly struck free-kick to beat England keeper Jordan Pickford.
Spurs failed to find a winner and the draw meant the north London outfit finished in fourth place in the Premier League table, with Chelsea leapfrogging them into third.