Micky van de Ven emerged as the first defender to net two goals in a Premier League game for Tottenham since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven nods into the net twice in opening period
The home side's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr scores final goal in dying moments
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Tottenham prolonged their unbeaten run in away games in the Premier League and handed the Toffees their initial loss at Hill Dickinson Stadium.
The Toffees were undefeated in their last five matches at their new ground at the dockside location, having left their historic home behind after more than a century at the end of the previous campaign.
But Spurs captain the Dutchman struck on two occasions from corners in the opening 45 minutes to put their strong form at jeopardy, and they were unable to turn it around before the midfielder - assisted by ex-Everton forward the Brazilian - headed home a final goal to put the game to bed.
The Everton defender believed he had levelled the tally a short while after the defender's opener, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, failed to convert a number of chances, while Vicario made a succession of fine stops to guarantee the London club went five away games unbeaten in the Premier League.
But the video assistant referee stepped in, advising the match official to check the score on the pitchside monitor and the official decided that the winger and the attacker were in an illegal position and had impeded with the Spurs keeper.
This victory moves the manager's team into third place in the Premier League, a handful of points off local foes and table-toppers Arsenal.
The Merseyside club remain 14th and are half a dozen points ahead of the drop zone.
After a drab weekday performance in the European competition against Monaco, where they managed a mere attempts on goal, the manager chose the French striker up front instead of ex-Everton forward Richarlison.
The new arrival was unable to influence the game before being replaced for Richarlison after an hour on the field, but it turns out he proved unnecessary in the end.
Defender Van de Ven transformed into an offensive threat to be reckoned with.
Tottenham's first goal came from a well-worked set-piece play, with the midfielder directing the ball toward the face of goal for an free Van de Ven to head home.
And the captain - stepping up as captain in the Argentine's absence - notched his next goal in first-half stoppage time as he outjumped the England keeper to nod in.
Van de Ven was equally impressive in defensive duties, partnering well with his defensive colleague as the pair dealt superbly with the 34 crosses thrown their way by the opposition.
Everton's new home had been a happy hunting ground, but it appears the novelty may have faded slightly and fans headed to the gates after the midfielder's final goal for Spurs.
The break in the team's winning streak at home won't be a massive concern for David Moyes, but their striker situation are.
Beto and the other striker - the Everton's pair of established strikers - had netted just a single goal combined before the weekend's outing.
And they were failed to contribute to that poor tally on a damp and dreary night on in Liverpool.
The striker's form was epitomized when he chose to overhead kick a clear chance from near the goal, even with having space and time to readjust for a simpler attempt that would have challenged the keeper.
The substitute, as well, was unable to make an impact after replacing Beto in the second half.
It was not for a lack of chance. Most of Everton's offensive moves came through the winger and the forward, who tirelessly whipped threatening crosses into the Tottenham box.
Everton: The team travel to Sunderland in the top flight on Monday, 3 November at 8 PM.
Spurs: The London club go to St James' Park on late October for their next round Carabao Cup match against Newcastle.
Lena Visser is a civil engineer and content writer specializing in foundation technology and sustainable construction practices.