Micky van de Ven Double Halts The Toffees' Run at Brand New Stadium
Micky van de Ven emerged as the initial defender to score two goals in a English top-flight match for Spurs since the Belgian defender in March 2013.
At a glance
Micky Van de Ven heads home twice in opening period
Everton's Jake O'Brien has equalizer disallowed after video check
Pape Matar Sarr scores final goal in dying moments
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Spurs prolonged their winning streak in away games in the Premier League and delivered Everton their initial loss at Hill Dickinson Stadium.
The Toffees were undefeated in their five previous fixtures 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 Van de Ven pounced twice from set-pieces in the first half to place their strong form at risk, and they were unable to mount a comeback before the midfielder - assisted by former Toffees attacker the Brazilian - nodded in a third to seal the victory.
Jake O'Brien believed he had levelled the scores a short while after the defender's opener, directing a powerful header past the Spurs keeper from an Everton corner.
The Portuguese striker, in the meantime, missed a handful of opportunities, while Vicario made a series of excellent saves to ensure the London club went five matches on the road unbeaten in the English top flight.
But the video assistant referee stepped in, instructing the match official to check the score on the pitchside monitor and the referee ruled that the winger and Iliman Ndiaye were in offside positions and had interfered with the Spurs keeper.
The win elevates Thomas Frank's team into third place in the Premier League, a handful of points off local foes and table-toppers Arsenal.
Everton remain in 14th position and sit half a dozen points ahead of the drop zone.
Tottenham analysis: The defender excels in duties at each end of pitch
After a uninspiring weekday performance in the European competition against the French side, where they managed a only attempts on goal, Frank opted for Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The new arrival was failed to make much of an impact before being substituted for the substitute after an hour on the pitch, but it turns out he proved unnecessary in the final outcome.
Defender the Dutchman converted into an attacking force to be feared.
Spurs' first goal came from a well-worked corner routine, with the midfielder directing the ball toward the face of goal for an free Van de Ven to score.
And the captain - stepping up as captain in the Argentine's absence - added his next goal in added time as he outjumped Jordan Pickford 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 numerous deliveries sent their way by the opposition.
Toffees breakdown: Everton missing finishing touch
Everton's recent stadium had been a fortress, but it seems the novelty may have worn off somewhat and supporters flocked to the exits after Sarr's third for Spurs.
The break in Everton's unbeaten home run will not be a massive worry for David Moyes, but their attacking woes are.
The forward and Thierno Barry - the Everton's pair of recognised centre-forwards - had netted just one league goal combined before Sunday's match.
And they were failed to contribute to that miserable record on a wet and gloomy night on in Liverpool.
Beto's form was epitomized when he chose to bicycle-kick a clear chance from near the goal, despite having space and time to readjust for a simpler shot that would have tested Vicario.
Barry, as well, was unable to make an impact after replacing the starter in the 65th minute.
It was not for a shortage of opportunity. The majority of the home side's offensive moves came through Grealish and Ndiaye, who tirelessly delivered dangerous crosses into the Spurs penalty area.
Upcoming fixtures for both teams?
Everton: Moyes' men head to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: The London club go to Newcastle's ground on late October for their fourth-round League Cup match against the Magpies.