Micky van de Ven Double Ends The Toffees' Run at New Home Ground
The Dutch defender emerged as the first backline player to net two goals in a English top-flight game for Spurs since Jan Vertonghen in spring 2013.
Match summary
The Spurs defender nods into the net twice in opening period
Everton's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr scores final goal in 89th minute
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender found the net on two occasions as Tottenham extended their winning streak on the road in the Premier League and delivered Everton their first defeat at their new home.
The Toffees were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after more than a century at the conclusion of the previous campaign.
But Tottenham's leader Van de Ven struck on two occasions from corners in the opening 45 minutes to put their impressive record at jeopardy, and they were unable to mount a comeback before the midfielder - set up by former Toffees attacker the Brazilian - nodded in a final goal to seal the victory.
Jake O'Brien thought he had levelled the scores five minutes after the defender's opener, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, in the meantime, missed a number of chances, while Vicario made a succession of fine saves to ensure the London club went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, instructing the match official to review the score on the screen and the referee ruled that the winger and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory moves Thomas Frank's team up to third in the division, five points off local foes and leaders Arsenal.
Everton remain 14th and are half a dozen points ahead of the relegation zone.
Tottenham analysis: The defender excels in duties at each end of pitch
After a drab weekday performance in the European competition against Monaco, where they mustered a only two shots on target, Frank chose the French striker up front instead of former Toffees player the Brazilian.
The summer signing was failed to make much of an impact before being substituted for the substitute after 60 minutes on the pitch, but it turns out he proved unnecessary in the end.
Defender the Dutchman transformed into an offensive threat to be feared.
Spurs' first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball toward the face of goal for an unmarked Van de Ven to score.
And Ven de Ven - stepping up as captain in the Argentine's absence - notched his second in added time as he rose above Jordan Pickford to head home.
Van de Ven was equally impressive in defensive duties, partnering effectively with Kevin Danso as the duo dealt excellently with the 34 crosses sent their way by the opposition.
Toffees breakdown: Everton lacking striker's instinct
The club's new home had been a happy hunting ground, but it seems the freshness may have worn off slightly and supporters headed to the gates after the midfielder's final goal for Spurs.
The break in Everton's unbeaten home run will not be a massive worry for the manager, but their striker situation will be.
The forward and the other striker - the Toffees' pair of recognised strikers - had netted just a single goal between them before Sunday's outing.
And they were unable to contribute to that poor record on a damp and dreary evening on Merseyside.
The striker's performance was summed up when he opted to bicycle-kick a clear chance from close range, even with having room and time to readjust for a simpler shot that would have tested the keeper.
Barry, as well, failed to influence the game after coming on for the starter in the 65th minute.
It wasn't for a lack of chance. Most of Everton's offensive moves came through the winger and the forward, who relentlessly delivered dangerous balls into the Tottenham penalty area.
Upcoming fixtures for both teams?
Everton: The team head to Sunderland in the top flight on Monday, 3 November at 20:00 GMT.
Tottenham: The London club go to St James' Park on Wednesday, 29 October for their next round Carabao Cup tie against the Magpies.