The Dutch defender became the initial backline player to score two goals in a English top-flight match for Spurs since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven heads into the net two times in opening period
Everton's defender has goal ruled after VAR review
Pape Matar Sarr scores third in dying moments
The defeat is Everton's first at their new ground
Micky van de Ven found the net on two occasions as Tottenham extended their unbeaten run in away games in the top division and handed the Toffees their first defeat at their new home.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of last season.
But Spurs captain Van de Ven pounced twice from corners in the first half to place their strong form at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker the Brazilian - nodded in a final goal to seal the victory.
The Everton defender believed he had equalized the tally five minutes after Van de Ven's opener, directing a bullet header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, missed a handful of opportunities, while Vicario made a succession of fine saves to guarantee the London club went five away games unbeaten in the Premier League.
But the VAR intervened, instructing the match official to check the score on the screen and the official decided that the winger and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory moves the manager's team up to third in the division, a handful of points off north London rivals and table-toppers the Gunners.
The Merseyside club stay in 14th position and are six points clear of the relegation zone.
After a drab weekday display in the European competition against Monaco, where they managed a mere attempts on goal, the manager chose Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The summer signing was failed 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 the Dutchman converted into an offensive threat to be reckoned with.
Spurs' opening strike came from a well-worked set-piece play, with Rodrigo Bentancur directing the ball back across the face of goal for an unmarked the defender to head home.
And Ven de Ven - stepping up as skipper in Cristian Romero's unavailability - added his second in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was equally outstanding in defence, combining well with Kevin Danso as the pair handled superbly with the numerous deliveries thrown their way by the opposition.
Everton's new home had been a fortress, but it appears the novelty may have faded slightly and fans headed to the exits after the midfielder's final goal for Tottenham.
The end in Everton's unbeaten home run won't be a major worry for David Moyes, but their striker situation are.
The forward and the other striker - the Everton's pair of established strikers - had netted only one league goal combined before Sunday's outing.
And they were unable to contribute to that miserable record on a wet and gloomy night on Merseyside.
Beto's form was epitomized when he chose to bicycle-kick a golden opportunity from near the goal, even with having space and time to readjust for a simpler shot that would have tested the keeper.
Barry, too, was unable to make an impact after coming on for Beto in the 65th minute.
It was not for a lack of chance. The majority of Everton's attacks came through Grealish and Ndiaye, who tirelessly delivered threatening balls into the Tottenham box.
Everton: Moyes' men head to Sunderland in the Premier League on early November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on late October for their fourth-round Carabao Cup match against Newcastle.