The Dutch defender became the initial backline player to net two goals in a Premier League game for Spurs since the Belgian defender in March 2013.
At a glance
The Spurs defender heads into the net twice in opening period
Everton's defender has goal disallowed after video check
Senegalese midfielder scores third in 89th minute
This loss is Everton's first at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Tottenham prolonged their unbeaten run in away games in the Premier League and handed Everton their first defeat at their new home.
The Toffees were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having left Goodison Park behind after more than a century at the conclusion of last season.
But Tottenham's leader the Dutchman pounced twice from corners in the opening 45 minutes to place their impressive record at risk, and they were failed to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker Richarlison - nodded in a third to seal the victory.
The Everton defender believed he had equalized the tally a short while after Van de Ven's opener, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a number of chances, while the Italian goalkeeper made a series of fine stops to guarantee Tottenham went five matches on the road unbeaten in the Premier League.
But the VAR intervened, instructing the match official to review the score on the pitchside monitor and the referee decided that Jack Grealish and Iliman Ndiaye were in offside positions and had interfered with the Tottenham goalkeeper.
This victory elevates Thomas Frank's side up to third in the division, a handful of points off north London rivals and table-toppers the Gunners.
Everton remain 14th and sit six points ahead of the drop zone.
Following a uninspiring weekday display in the European competition against the French side, where they mustered a only two shots on target, Frank chose Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The new arrival was failed to influence the game before being substituted for Richarlison after an hour on the pitch, but it turns out he wasn't needed in the end.
Defender Van de Ven transformed into an attacking force to be feared.
Spurs' opening strike came from a well-worked corner routine, with the midfielder directing the ball toward the face of goal for an free the defender to head home.
And Ven de Ven - stepping up as skipper in Cristian Romero's unavailability - added his next goal in added time as he outjumped Jordan Pickford to head home.
The Dutchman was equally outstanding in defensive duties, combining effectively with Kevin Danso as the duo dealt superbly with the numerous deliveries sent their way by Everton.
The club's recent stadium had been a happy hunting ground, but it seems the freshness may have faded slightly and supporters headed to the gates after the midfielder's final goal for Spurs.
The break in Everton's unbeaten home run will not be a massive worry for David Moyes, but their striker situation will be.
The forward and the other striker - the Everton's pair of established strikers - had scored only one league goal combined before Sunday's outing.
And they were failed to add to that poor record on a damp and dreary night on in Liverpool.
Beto's form was summed up when he chose to overhead kick a golden opportunity from close range, even with having space and time to reposition for a simpler attempt that would have tested the keeper.
The substitute, too, was unable to make an impact after coming on for the starter in the second half.
It wasn't for a lack of opportunity. The majority of the home side's offensive moves came through the winger and Ndiaye, who relentlessly delivered dangerous crosses into the Spurs penalty area.
Everton: The team head to Sunderland in the top flight on early November at 8 PM.
Spurs: Spurs go to St James' Park on late October for their fourth-round League Cup tie against the Magpies.
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