The Toffees equalised on the half hour mark with Jack Harrison awarded the leveller following a corner, before Richarlison brilliantly restored Spurs' lead just before the break from the edge of the box.
Everton secured a late draw went Branthwaite nodded the ball home in the back-post, after Cristian Romero inadvertenly flicked on a free kick in the fourth minute of stoppage time.
Mail Sport's Lewis Steele gives his verdict on the players in his match ratings.
Jarrad Branthwaite scored in injury-time to rescue a point for Everton against Tottenham
Richarlison returned to his former club and scored a brilliant brace at Goodison Park
Jordan Pickford 7: The Toffees goalkeeper was helpless in stopping two brilliant strikes by Richarlison but made important saves to give his side home.
Ben Godfrey 7: His header across goal from a deep corner led to the Everton's first equaliser.
James Tarkowski 6.5: Could have gone tighter to block Udogie's cross for the opener.
Jarrad Branthwaite 7: The biggest success story of the Dyche era, he made sure it was him and not Richarlison grabbing the headlines with a late goal.
Vitaliy Mykolenko 6: The full back handled Brennan Johnson well throughout the clash.
Branthwaite's late header ensured it wasn't Richarlison who took all the headlines
Dwight McNeil (pictured) and James Garner delivered corners which causes Spurs problems
James Garner 6.5: Delivered some inswinging corners which caused Spurs trouble throughout the match.
Idrissa Gueye 6: Made a poor decision to take a shoot from the edge of the box after breaking through the Tottenham midfield.
Ashley Young 6: Wasn't involved as much as he would have like before being replaced by teenager Youssef Chermiti.
Jack Harrison 6.5: He goes down as the goalscorer for the opener but he might not have known much about it.
Dwight Mcneil 6.5: Like Garner from the other side, he delivered some superb corners to creat havoc in the Tottenham penalty area.
Dominic Calvert-Lewin 7: Bright display from the striker but his goal drought continues after Harrison was awarded a goal he thought he'd scored.
Jack Harrison has been awarded Everton's equaliser to the disappointment of Calvert-Lewin
Guglielmo Vicario 6: Similar to last week's FA Cup defeat to Manchester City, the Italian was pushed around too easily at set pieces.
Pedro Porro 6: He was unusually quiet and didn't get on the ball as much as he usually does.
Cristian Romero 6.5: His flicked header from a late free kick fell invitingly for Branthwaite to score the equaliser.
Van de Ven 7.5: A superb performance from the Dutchman, who looked as fast and strong as ever.
Destiny Udogie 7: Looked like a threat every time he came forward and managed to get an assist.
Similar to last week's loss to Manchester City, Vicario was pushed around too easily
Van de Ven was as fast and strong as ever against a physical Calvert-Lewin
Rodrigo Bentancur 7: Kept Tottenham ticking with some good passes from midfield before being replaced in the second half.
Pierre Emile-Hojbjerg 7: The Danish midfielder was strong and made good tackles again.
Brennan Johnson 7: Relatively quiet down the right.
James Maddison 7.5: An excellent performance from the England international, including a superb pass to Richarlison for the second goal.
Timo Werner 7.5: Looked dangerous down the left wing and his pace caused problems for Everton. Should have done better to bury a big chance in the second half.
Richarlison 8: Was the best player on the pitch as he showed his old employers what they are missing with an impressive brace.
Richarlison was the best player on the pitch as he showed his old employers what they are missing
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