The Dutch defender became the initial backline player to score twice in a Premier League match for Spurs since the Belgian defender in March 2013.
Key points
Micky Van de Ven heads home two times in opening period
The home side's defender has goal ruled after video check
Pape Matar Sarr nets final goal in dying moments
This loss is Everton's initial at their new ground
The Tottenham defender found the net on two occasions as Tottenham prolonged their winning streak in away games in the Premier League and delivered the Toffees their initial loss at their new home.
The Toffees were undefeated in their last five matches at their new ground at Bramley-Moore Dock, having departed their historic home behind after more than a century at the end of last season.
But Tottenham's leader Van de Ven struck on two occasions from set-pieces in the opening 45 minutes to put their strong form at risk, and they were unable to mount a comeback before the midfielder - assisted by ex-Everton forward Richarlison - headed home a final goal to put the game to bed.
The Everton defender believed he had equalized the scores five minutes after the defender's opener, glancing a powerful header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, missed a handful of opportunities, while Vicario made a succession of fine stops to guarantee the London club went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, instructing the match official to review the score on the pitchside monitor and the referee decided that Jack Grealish and the attacker were in an illegal position and had interfered with the Spurs keeper.
This victory elevates the manager's side up to third in the Premier League, a handful of points off north London rivals and leaders Arsenal.
Everton remain in 14th position and sit six points clear of the relegation zone.
Following a drab weekday display in the European competition against Monaco, where they managed a mere two shots on goal, the manager chose Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The summer signing 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 final outcome.
Centre-back Van de Ven converted into an attacking force to be feared.
Spurs' first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball back across the six-yard box for an free Van de Ven to score.
And the captain - stepping up as skipper in Cristian Romero's absence - added his next goal in added time as he rose above Jordan Pickford to head home.
Van de Ven was just as impressive in defence, combining effectively with Kevin Danso as the pair handled superbly with the numerous deliveries thrown their way by Everton.
Everton's new home had been a fortress, but it seems the novelty may have worn off slightly and fans flocked to the gates after Sarr's third for Spurs.
The break in Everton's winning streak at home will not be a major worry for the manager, but their striker situation will be.
The forward and the other striker - the Toffees' pair of established strikers - had scored only one league goal between them before the weekend's outing.
And they were failed to add to that poor record on a damp and dreary night on in Liverpool.
The striker's performance was epitomized when he chose to bicycle-kick a golden opportunity from near the goal, despite having room and opportunity to reposition for a simpler attempt that would have challenged Vicario.
Barry, as well, was unable to make an impact after replacing Beto in the 65th minute.
It wasn't for a lack of chance. Most of Everton's offensive moves came through the winger and Ndiaye, who relentlessly whipped threatening balls into the Spurs box.
Everton: Moyes' men head to Sunderland in the top flight on Monday, 3 November at 8 PM.
Spurs: Spurs travel to Newcastle's ground on late October for their fourth-round Carabao Cup tie against the Magpies.
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