Micky van de Ven Double Ends The Toffees' Run at Brand New Home Ground
Micky van de Ven became the initial backline player to net twice in a Premier League game for Spurs since Jan Vertonghen in spring 2013.
At a glance
Micky Van de Ven nods into the net two times in first half
The home side's Jake O'Brien has goal disallowed after video check
Pape Matar Sarr nets final goal in dying moments
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven found the net twice as Spurs extended their unbeaten run in away games in the Premier League and delivered Everton their initial loss at their new home.
Everton were unbeaten in their last five matches at their recently opened stadium at Bramley-Moore Dock, having left their historic home behind after more than a century at the conclusion of last season.
But Tottenham's leader the Dutchman pounced on two occasions from set-pieces in the first half to place their impressive record at jeopardy, and they were failed to turn it around before Pape Matar Sarr - assisted by former Toffees attacker Richarlison - nodded in a third to put the game to bed.
Jake O'Brien thought he had levelled the tally a short while after Van de Ven's opener, glancing a bullet header past Guglielmo Vicario from an set-piece.
The Portuguese striker, meanwhile, failed to convert a number of opportunities, while Vicario made a succession of excellent stops to guarantee Tottenham went five away games unbeaten in the Premier League.
But the VAR intervened, instructing the match official to check the score on the screen and the official decided that Jack Grealish and the attacker were in an illegal position and had impeded with the Spurs keeper.
This victory elevates the manager's side into third place in the Premier League, five points off local foes and leaders the Gunners.
Everton remain in 14th position and are half a dozen points ahead of the drop zone.
Tottenham analysis: Van de Ven fulfils role at both ends of pitch
After a uninspiring weekday display in the European competition against the French side, where they managed a mere attempts on goal, Frank opted for the French striker in attack instead of ex-Everton forward the Brazilian.
The summer signing was unable to influence the game before being replaced for the substitute after 60 minutes on the field, but it turns out he wasn't needed in the final outcome.
Centre-back the Dutchman transformed into an offensive threat to be feared.
Spurs' first goal came from a cleverly executed set-piece play, with the midfielder heading the ball back across the six-yard box for an free the defender to score.
And Ven de Ven - 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.
The Dutchman was just as outstanding in defensive duties, combining well with his defensive colleague as the duo handled excellently with the 34 crosses sent their way by Everton.
Everton analysis: Everton missing finishing touch
The club's new home had been a happy hunting ground, but it appears the novelty may have faded slightly and fans headed to the exits after the midfielder's third for Spurs.
The end in the team's winning streak at home will not be a massive concern for David Moyes, but their striker situation are.
Beto and Thierno Barry - the Toffees' two established centre-forwards - had netted just one league goal combined before Sunday's match.
And they were unable to add to that miserable record on a wet and gloomy evening on in Liverpool.
The striker's performance was summed up when he chose to bicycle-kick a clear chance from near the goal, even with having space and time to readjust for a more conventional attempt that would have challenged Vicario.
The substitute, as well, was unable to influence the game after coming on for the starter in the 65th minute.
It was not for a lack of chance. The majority of the home side's attacks came through the winger and the forward, who tirelessly delivered dangerous crosses into the Tottenham penalty area.
What next for these two sides?
The Toffees: Moyes' men travel to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: The London club go to St James' Park on Wednesday, 29 October for their fourth-round League Cup tie against the Magpies.