Micky van de Ven Double Ends Everton's Run at Brand New Stadium
The Dutch defender became the first defender to score two goals in a Premier League game for Spurs since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven nods into the net two times in opening period
The home side's Jake O'Brien has equalizer disallowed after VAR review
Pape Matar Sarr nets final goal in 89th minute
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Spurs extended their winning streak in away games in the top division and delivered Everton their initial loss at their new home.
The Toffees were unbeaten in their five previous fixtures at their recently opened stadium at the dockside location, having departed Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Tottenham's leader the Dutchman struck twice from set-pieces in the opening 45 minutes to place their impressive record at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker the Brazilian - nodded in a final goal to put the game to bed.
Jake O'Brien believed he had equalized the tally a short while after the defender's opener, glancing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, failed to convert a number of opportunities, while the Italian goalkeeper made a succession of fine saves to ensure Tottenham went five matches on the road without defeat in the English top flight.
But the VAR stepped in, instructing the match official to check the goal on the pitchside monitor and the referee ruled that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Spurs keeper.
This victory elevates the manager's team up to third in the Premier League, five points off local foes and table-toppers the Gunners.
Everton remain 14th and sit half a dozen points ahead of the relegation zone.
Tottenham analysis: Van de Ven fulfils role at each end of the field
After a drab midweek display in the European competition against the French side, where they mustered a mere two shots on goal, the manager opted for Randal Kolo Muani up front instead of former Toffees player the Brazilian.
The new arrival was unable to make much of an impact before being replaced for the substitute after an hour on the pitch, but it emerged he proved unnecessary in the end.
Defender Van de Ven converted into an offensive threat to be feared.
Spurs' opening strike came from a well-worked set-piece play, with Rodrigo Bentancur heading 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 - notched his second in first-half stoppage time as he outjumped the England keeper to head home.
Van de Ven was equally impressive in defence, partnering effectively with his defensive colleague as the pair handled superbly with the numerous deliveries thrown their way by the opposition.
Toffees breakdown: Everton lacking finishing touch
Everton's recent stadium had been a fortress, but it appears the freshness may have worn off somewhat and fans headed to the exits after the midfielder's third for Tottenham.
The break in the team's winning streak at home won't be a major worry for David Moyes, but their striker situation are.
The forward and Thierno Barry - the Everton's pair of recognised strikers - had netted just one league goal combined before Sunday's outing.
And they were unable to add to that poor record on a damp and dreary night on Merseyside.
The striker's form was epitomized when he chose to bicycle-kick a golden opportunity from near the goal, despite having room and time to readjust for a more conventional attempt that would have tested the keeper.
Barry, too, was unable to influence the game after coming on for Beto in the second half.
It wasn't for a lack of chance. The majority of Everton's offensive moves came through Grealish and Ndiaye, who tirelessly delivered dangerous balls into the Spurs box.
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: Spurs go to St James' Park on Wednesday, 29 October for their next round Carabao Cup tie against the Magpies.