The Dutch defender emerged as the first defender to net two goals in a English top-flight match for Tottenham since the Belgian defender in March 2013.
At a glance
The Spurs defender heads home twice in first half
Everton's defender has equalizer disallowed after video check
Senegalese midfielder nets final goal in 89th minute
The defeat is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Tottenham extended their winning streak in away games in the top division and handed the Toffees their initial loss at Hill Dickinson Stadium.
The Toffees were undefeated in their five previous fixtures at their new ground at the dockside location, having departed Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Spurs captain the Dutchman struck on two occasions from set-pieces in the opening 45 minutes to put their impressive record at jeopardy, and they were failed to mount a comeback before the midfielder - set up by ex-Everton forward Richarlison - headed home a third to put the game to bed.
Jake O'Brien thought he had equalized the tally five minutes after Van de Ven's opener, glancing a bullet header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, missed a number of chances, while the Italian goalkeeper made a series of fine saves to ensure Tottenham went five matches on the road without defeat in the Premier League.
But the VAR stepped in, instructing Craig Pawson to review the score on the pitchside monitor and the referee decided that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory elevates the manager's team into third place in the Premier League, a handful of points off north London rivals and table-toppers the Gunners.
The Merseyside club remain 14th and are half a dozen points ahead of the drop zone.
After a drab weekday performance in the European competition against Monaco, where they managed a only attempts on target, Frank chose Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The new arrival was failed to influence the game before being replaced for the substitute after an hour on the pitch, but it turns out he proved unnecessary in the end.
Centre-back Van de Ven converted into an attacking force to be reckoned with.
Spurs' first goal came from a well-worked corner routine, with Rodrigo Bentancur heading the ball back across the six-yard box for an free the defender to score.
And the captain - stepping up as captain in the Argentine's absence - notched his next goal in added time as he rose above the England keeper to head home.
Van de Ven was just as impressive in defensive duties, partnering well with Kevin Danso as the duo handled excellently with the numerous deliveries thrown their way by Everton.
The club's new home had been a happy hunting ground, but it seems the freshness may have faded slightly and supporters flocked to the gates after the midfielder's third for Spurs.
The break in Everton's winning streak at home will not be a massive worry for the manager, but their attacking woes will be.
Beto and the other striker - the Toffees' pair of established strikers - had netted just a single goal combined before Sunday's match.
And they were failed to contribute to that miserable tally on a wet and gloomy evening on Merseyside.
The striker's form was summed up when he chose to bicycle-kick a clear chance from close range, even with having space and opportunity to reposition for a more conventional shot that would have challenged the keeper.
The substitute, too, failed to make an impact after replacing the starter in the 65th minute.
It was not for a shortage of chance. The majority of Everton's offensive moves came through Grealish and Ndiaye, who tirelessly whipped threatening balls into the Spurs penalty area.
The Toffees: The team head to the Stadium of Light in the top flight on early November at 8 PM.
Spurs: Spurs travel to St James' Park on Wednesday, 29 October for their fourth-round Carabao Cup tie against Newcastle.
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