Van de Ven Double Halts The Toffees' Run at New Home Ground
The Dutch defender became the first backline player to net twice in a Premier League game for Tottenham since Jan Vertonghen in March 2013.
Match summary
Micky Van de Ven heads into the net twice in opening period
The home side's defender has goal ruled after video check
Pape Matar Sarr nets final goal in 89th minute
The defeat is the Merseyside club's initial at their new ground
Micky van de Ven found the net twice as Spurs extended their unbeaten run in away games in the top division and delivered the Toffees their first defeat at Hill Dickinson Stadium.
Everton were unbeaten 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 the previous campaign.
But Tottenham's leader Van de Ven pounced on two occasions from corners in the first half to place their strong form at risk, and they were failed to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - nodded in a third to seal the victory.
The Everton defender thought he had levelled the scores a short while after Van de Ven's opener, directing a powerful header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, failed to convert a handful of chances, while Vicario made a succession of fine saves to guarantee Tottenham went five away games unbeaten in the English top flight.
But the video assistant referee intervened, instructing the match official to review the score on the pitchside monitor and the official ruled that Jack Grealish and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's side up to third in the division, a handful of points off local foes and table-toppers Arsenal.
Everton remain 14th and sit six points ahead of the relegation zone.
Tottenham analysis: The defender excels in role at each end of the field
After a uninspiring weekday display in the European competition against the French side, where they mustered a only two shots on goal, Frank chose the French striker up front instead of former Toffees player the Brazilian.
The new arrival was failed to make much of an impact before being replaced for the substitute after an hour on the pitch, but it emerged he wasn't needed in the end.
Centre-back the Dutchman converted into an offensive threat to be reckoned with.
Tottenham's first goal came from a cleverly executed corner routine, with Rodrigo Bentancur heading the ball back across the six-yard box for an free Van de Ven to score.
And Ven de Ven - filling in as captain in Cristian Romero's unavailability - notched his second in first-half stoppage time as he rose above the England keeper to head home.
Van de Ven was equally impressive in defensive duties, combining effectively with his defensive colleague as the duo dealt superbly with the 34 crosses sent their way by Everton.
Everton analysis: Everton lacking finishing touch
The club's recent stadium had been a fortress, but it seems the novelty may have faded somewhat and fans headed to the gates after Sarr's third for Tottenham.
The end in the team's winning streak at home won't be a massive worry for the manager, but their striker situation will be.
The forward and the other striker - the Toffees' two recognised centre-forwards - had scored just a single goal between them before the weekend's match.
And they were unable to contribute to that poor record on a wet and gloomy night on in Liverpool.
The striker's performance was epitomized when he chose to overhead kick a golden opportunity from near the goal, despite having space and time to reposition for a more conventional shot that would have challenged Vicario.
The substitute, as well, failed to make an impact after coming on for the starter in the 65th minute.
It wasn't for a lack of opportunity. The majority of Everton's offensive moves came through the winger and the forward, who tirelessly delivered dangerous balls into the Spurs box.
What next for both teams?
The Toffees: The team travel to the Stadium of Light in the top flight on Monday, 3 November at 20:00 GMT.
Spurs: Spurs travel to Newcastle's ground on late October for their fourth-round League Cup match against the Magpies.