Van de Ven Double Ends The Toffees' Run at New Stadium
The Dutch defender became the initial defender to score two goals in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
Match summary
Micky Van de Ven nods home two times in first half
Everton's Jake O'Brien has equalizer ruled after VAR review
Senegalese midfielder scores final goal in dying moments
This loss is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender found the net twice as Spurs extended their winning streak on the road in the top division and delivered Everton their initial loss at their new home.
The Toffees were unbeaten in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed their historic home behind after 133 years at the end of last season.
But Spurs captain the Dutchman struck on two occasions from set-pieces in the first half to place their strong form at jeopardy, and they were failed to turn it around before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - nodded in a third to put the game to bed.
Jake O'Brien thought he had equalized the tally a short while after the defender's opener, glancing a powerful header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a handful of chances, while Vicario made a series of fine saves to ensure the London club went five away games without defeat in the Premier League.
But the VAR stepped in, instructing the match official to check the score on the pitchside monitor and the official decided that Jack Grealish and Iliman Ndiaye were in offside positions and had impeded with the Tottenham goalkeeper.
The win elevates the manager's team into third place in the division, five points off local foes and table-toppers the Gunners.
Everton stay in 14th position and sit six points ahead of the relegation zone.
Tottenham analysis: Van de Ven fulfils role at both ends of the field
After a uninspiring weekday display in the European competition against Monaco, where they managed a mere attempts on target, Frank chose the French striker in attack instead of former Toffees player Richarlison.
The new arrival was unable to make much of an impact before being substituted for Richarlison after 60 minutes on the pitch, but it emerged he wasn't needed in the final outcome.
Defender Van de Ven transformed into an offensive threat to be reckoned with.
Tottenham's first goal came from a well-worked corner routine, with the midfielder heading the ball back across the face of goal for an unmarked the defender to score.
And the captain - stepping up as skipper in Cristian Romero's absence - notched his second in first-half stoppage time as he rose above Jordan Pickford to nod in.
Van de Ven was equally outstanding in defence, partnering effectively with his defensive colleague as the duo dealt superbly with the numerous deliveries sent their way by Everton.
Toffees breakdown: Everton missing striker's instinct
Everton's recent stadium had been a happy hunting ground, but it appears the freshness may have worn off somewhat and fans flocked to the exits after the midfielder's final goal for Tottenham.
The end in the team's winning streak at home won't be a major worry for David Moyes, but their striker situation are.
Beto and Thierno Barry - the Toffees' pair of recognised centre-forwards - had netted only one league goal combined before the weekend's outing.
And they were unable to contribute to that poor tally on a wet and gloomy night on in Liverpool.
The striker's form was epitomized when he opted to bicycle-kick a clear chance from close range, even with having room and opportunity to readjust for a simpler attempt that would have tested the keeper.
The substitute, too, was unable to influence the game after replacing Beto in the 65th minute.
It was not for a shortage of opportunity. Most of the home side's offensive moves came through Grealish and Ndiaye, who tirelessly whipped threatening balls into the Spurs box.
Upcoming fixtures for these two sides?
The Toffees: Moyes' men travel to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: Spurs travel to Newcastle's ground on late October for their fourth-round League Cup tie against Newcastle.