The Dutch defender emerged as the initial backline player to net twice in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
Key points
The Spurs defender heads home twice in first half
The home side's Jake O'Brien has equalizer disallowed after video check
Senegalese midfielder scores third in dying moments
This loss is the Merseyside club's initial at their new ground
The Tottenham defender scored twice as Spurs extended their unbeaten run in away games in the Premier League and handed the Toffees their first defeat at their new home.
The Toffees were undefeated in their last five matches at their recently opened stadium at the dockside location, having departed their historic home behind after 133 years at the end of the previous campaign.
But Spurs captain the Dutchman struck twice from corners in the opening 45 minutes to put their strong form at jeopardy, and they were unable to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - nodded in a final goal to seal the victory.
The Everton defender believed he had levelled the tally a short while after the defender's opener, directing a bullet header past Guglielmo Vicario from an set-piece.
Beto, in the meantime, missed a number of chances, while Vicario made a succession of fine saves to ensure Tottenham went five away games without defeat in the English top flight.
But the VAR intervened, instructing the match official to review the goal on the pitchside monitor and the referee decided that Jack Grealish 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, five points off local foes and table-toppers the Gunners.
The Merseyside club stay 14th and sit half a dozen points ahead of the relegation zone.
After a drab midweek performance in the European competition 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 the Brazilian.
The summer signing was unable to make much of an impact before being substituted for Richarlison after 60 minutes on the field, but it turns out he wasn't needed in the final outcome.
Defender the Dutchman converted into an offensive threat to be feared.
Spurs' opening strike came from a well-worked corner routine, with the midfielder heading the ball toward the face of goal for an unmarked Van de Ven to head home.
And Ven de Ven - stepping up as skipper in the Argentine's absence - notched his next goal in added time as he outjumped Jordan Pickford to head home.
Van de Ven was equally outstanding in defence, partnering effectively with Kevin Danso as the duo handled superbly with the 34 crosses sent their way by Everton.
The club's new home had been a fortress, but it appears the freshness may have worn off slightly and fans headed to the gates after the midfielder's final goal for Tottenham.
The end in the team's winning streak at home will not be a massive worry for the manager, but their striker situation are.
Beto and Thierno Barry - the Everton's pair of recognised centre-forwards - had netted only one league goal combined before Sunday's outing.
And they were failed to contribute to that poor tally on a wet and gloomy night on Merseyside.
The striker's performance was epitomized when he opted to bicycle-kick a clear chance from close range, even with having space and time to readjust for a simpler shot that would have tested Vicario.
The substitute, as well, failed to influence the game after replacing the starter in the second half.
It was not for a shortage of chance. The majority of the home side's offensive moves came through the winger and Ndiaye, who tirelessly whipped threatening balls into the Tottenham box.
Everton: The team travel to Sunderland in the top flight on early November at 8 PM.
Spurs: The London club go to Newcastle's ground on late October for their next round League Cup match against the Magpies.
Liam Hendricks is a seasoned gambling analyst and writer with over a decade of experience covering online casinos.