Micky van de Ven Double Ends The Toffees' Unbeaten Streak at New Stadium
Micky van de Ven emerged as the first backline player to score twice in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven heads into the net two times in first half
Everton's Jake O'Brien has goal disallowed after VAR review
Pape Matar Sarr nets third in dying moments
The defeat is the Merseyside club's initial at their new ground
The Tottenham defender scored on two occasions as Tottenham prolonged their unbeaten run on the road in the top division and delivered Everton their first defeat at their new home.
Everton were undefeated in their five previous fixtures at their recently opened stadium at the dockside location, having departed Goodison Park behind after more than a century at the end of last season.
But Spurs captain Van de Ven struck on two occasions from corners in the opening 45 minutes to put their impressive record at risk, and they were failed to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker Richarlison - headed home a final goal to seal the victory.
Jake O'Brien believed he had levelled the scores five minutes after the defender's first goal, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, missed a number of chances, while Vicario made a succession of excellent saves to ensure the London club went five away games without defeat in the Premier League.
But the VAR stepped in, instructing the match official to review the score on the screen and the official decided that Jack Grealish and Iliman Ndiaye were in an illegal position and had interfered with the Spurs keeper.
The win moves Thomas Frank's side into third place in the Premier League, five points off north London rivals and table-toppers the Gunners.
Everton stay 14th and are six points ahead of the relegation zone.
Tottenham analysis: The defender fulfils duties at both ends of the field
After a uninspiring weekday display in the Champions League against Monaco, where they managed a only two shots on target, the manager opted for Randal Kolo Muani up front instead of former Toffees player Richarlison.
The new arrival was unable to influence the game before being substituted for the substitute after an hour on the field, but it emerged he proved unnecessary in the end.
Centre-back Van de Ven converted into an offensive threat to be feared.
Spurs' opening strike came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball back across the face of goal for an unmarked the defender to head home.
And the captain - stepping up as captain in Cristian Romero's absence - added his next goal in added time as he outjumped the England keeper to head home.
The Dutchman was just as outstanding in defence, combining effectively with Kevin Danso as the pair dealt excellently with the 34 crosses sent their way by the opposition.
Toffees breakdown: Toffees lacking finishing touch
The club's new home had been a fortress, but it appears the novelty may have worn off slightly and fans flocked to the gates after Sarr's final goal for Tottenham.
The break in Everton's unbeaten home run will not be a massive concern for the manager, but their striker situation are.
The forward and Thierno Barry - the Everton's pair of established centre-forwards - had scored only one league goal combined before the weekend's outing.
And they were unable to contribute to that poor record on a wet and gloomy night on in Liverpool.
Beto's form was epitomized when he opted to overhead kick a clear chance from near the goal, even with having space and opportunity to reposition for a simpler attempt that would have challenged Vicario.
The substitute, too, was unable to influence the game after replacing Beto in the 65th minute.
It wasn't for a lack of chance. Most of Everton's attacks came through the winger and the forward, who relentlessly whipped dangerous balls into the Spurs box.
Upcoming fixtures for both teams?
The Toffees: The team head to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: Spurs travel to St James' Park on late October for their fourth-round Carabao Cup match against Newcastle.