Richarlison's clinical finishing against his former team looked to have won Spurs this match, with the Brazilian scoring first-half goals either side of a scrappy Everton equaliser scored by Jack Harrison.
A lack of quality in the final third made the second half a more stop-start affair, but Everton equalised in the fourth minute of added time to deny Ange Postecoglou's side victory at the death.
Dom Smith was on hand to rate the Tottenham players' displays...
Guglielmo Vicario 5
Just like for Nathan Ake's late winner for Manchester City a week ago, the goalkeeper was not strong enough when put under pressure by Everton. They exploited that, scoring through Harrison, before he then raised his level.
Pedro Porro 5
Didn't get close enough to Vitalii Mykolenko when the Toffees were attacking, allowing the Ukrainian to roam free and cross.
Cristian Romero 7
Jostled with Everton's forward players and continued his excellent partnership with Micky van de Ven. A physical presence at the back, limiting the Toffees' chances.
Micky van de Ven 8
Showed his incredible recovery pace to make up ground and slide in on Dominic Calvert-Lewin in the first half. The same happened after the break when Jack Harrison sprinted clear.
Destiny Udogie 7
Assisted the opening goal by Richarlison and had one lung-busting run where he ran the length of the pitch and picked out a cross.
Pierre-Emile Hojbjerg 5
Busy in midfield, but too often shot wastefully from range when he should have passed instead.
Rodrigo Bentancur 5
Did OK in midfield before being replaced for Pape Matar Sarr. Not as involved as he usually is.
Brennan Johnson 5
Some nice touches, but this was a day when other attackers came to the fore for Spurs.
James Maddison 7
An impressive display by the England midfielder, who assisted Richarlison's second and could have scored midway through the second half when Jordan Pickford parried his half-volley.
Timo Werner 6
Involved in the opener for his new team, but should have put victory beyond doubt in the second half, instead squandering a huge opportunity.
Tottenham's best player on the afternoon. Lovely swept finish for his first goal, then a stunning right-foot curler into the top corner for the second. Did plenty of running and harrying too. Oustanding.
Pape Matar Sarr (Bentancur, 64') 5
Put himself about in a scrappy period of the match.
Dejan Kulusevski (Johnson, 64') 6
Had a few jinking runs as an important late outlet for Spurs.
Oliver Skipp (Werner, 86') N/A
Bryan Gil (Maddison, 86') N/A
Radu Dragusin (Hojbjerg, 89') N/A
Not used: Forster, Royal, Davies, Scarlett