The Dutch defender emerged as the first defender to net twice in a Premier League match for Spurs since Jan Vertonghen in March 2013.
At a glance
The Spurs defender heads into the net twice in opening period
The home side's Jake O'Brien has goal disallowed after video check
Senegalese midfielder scores third in dying moments
The defeat is Everton's initial at their new ground
The Tottenham defender scored on two occasions as Spurs extended their unbeaten run on the road in the Premier League and delivered the Toffees their initial loss at their new home.
Everton were undefeated in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having left Goodison Park behind after more than a century at the end of the previous campaign.
But Tottenham's leader Van de Ven pounced on two occasions from set-pieces in the first half to put their strong form at jeopardy, and they were failed to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - headed home a final goal to seal the victory.
The Everton defender believed he had equalized the scores a short while after the defender's opener, glancing a bullet header past Guglielmo Vicario from an set-piece.
The Portuguese striker, meanwhile, missed a number of chances, while Vicario made a succession of fine saves to ensure the London club went five away games without defeat in the English top flight.
But the video assistant referee intervened, advising the match official to check the goal on the screen and the official decided that the winger and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
The win moves the manager's side up to third in the division, five points off local foes and leaders Arsenal.
Everton stay 14th and are six points ahead of the drop zone.
Following a drab weekday performance in the European competition against the French side, where they managed a only two shots on target, the manager chose Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The summer signing was unable to make much of an impact before being replaced for the substitute after 60 minutes on the pitch, but it turns out he wasn't needed in the end.
Centre-back the Dutchman converted into an attacking force to be reckoned with.
Spurs' first goal came from a well-worked set-piece play, with the midfielder heading the ball back across the face of goal for an free Van de Ven to score.
And Ven de Ven - stepping up as captain in the Argentine's unavailability - notched his next goal in added time as he rose above the England keeper to nod in.
The Dutchman was just as outstanding in defence, combining well with his defensive colleague as the pair dealt superbly with the 34 crosses thrown 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 Sarr's third for Tottenham.
The end in the team's winning streak at home will not be a major worry for the manager, but their attacking woes will be.
The forward and Thierno Barry - the Toffees' pair of recognised strikers - had scored only one league goal between them before the weekend's match.
And they were failed to add to that miserable tally on a damp and dreary evening on Merseyside.
Beto's form was summed up when he opted to bicycle-kick a golden opportunity from near the goal, even with having room and time to readjust for a more conventional attempt that would have tested Vicario.
The substitute, as well, 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 the forward, who relentlessly delivered dangerous crosses into the Tottenham box.
Everton: Moyes' men travel to Sunderland in the top flight on Monday, 3 November at 8 PM.
Tottenham: The London club travel to St James' Park on late October for their fourth-round League Cup match against the Magpies.
Elara Vance is a seasoned business analyst with over a decade of experience covering international markets and industrial transformations.