Micky van de Ven became the initial defender to net two goals in a Premier League match for Tottenham since the Belgian defender in spring 2013.
At a glance
Micky Van de Ven heads into the net two times in first half
The home side's defender has equalizer disallowed after VAR review
Pape Matar Sarr nets final goal in 89th minute
This loss is Everton's initial at their new ground
The Tottenham defender scored twice as Spurs prolonged their unbeaten run on the road in the Premier League and delivered the Toffees their first defeat at their new home.
Everton were unbeaten in their last five matches at their new ground at the dockside location, having left their historic home behind after 133 years at the conclusion of the previous campaign.
But Spurs captain the Dutchman struck on two occasions from corners in the opening 45 minutes to put their impressive record at risk, and they were unable to mount a comeback before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - nodded in a third to put the game to bed.
The Everton defender thought he had levelled the scores five minutes after Van de Ven's opener, glancing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, failed to convert a number of opportunities, while Vicario made a succession of excellent saves to ensure the London club went five away games unbeaten in the Premier League.
But the VAR intervened, advising Craig Pawson to review the goal on the pitchside monitor and the referee 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 north London rivals and leaders Arsenal.
Everton remain in 14th position and sit six points clear of the drop zone.
Following a uninspiring weekday display in the Champions League against the French side, where they mustered a mere two shots on goal, the manager opted for Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The summer signing was failed to make much of an impact before being replaced for Richarlison after an hour on the field, but it turns out he wasn't needed in the final outcome.
Defender Van de Ven converted into an offensive threat to be feared.
Tottenham's first goal came from a well-worked set-piece play, with the midfielder heading the ball toward the face of goal for an free the defender to score.
And the captain - filling in as skipper in Cristian Romero's unavailability - added his second in first-half stoppage time as he rose above Jordan Pickford to head home.
Van de Ven was just as outstanding in defensive duties, partnering well with Kevin Danso as the duo handled excellently with the 34 crosses sent their way by Everton.
The club's new home had been a fortress, but it appears the novelty may have worn off slightly and fans headed to the gates after the midfielder's third for Tottenham.
The break in the team's winning streak at home won't be a major worry for the manager, but their attacking woes will be.
Beto and the other striker - the Toffees' two established centre-forwards - had netted only one league goal between them before the weekend's match.
And they were unable to contribute to that miserable record on a damp and dreary night on in Liverpool.
The striker's performance was summed up when he opted to bicycle-kick a clear chance from close range, despite having room and time to reposition for a more conventional shot that would have tested the keeper.
Barry, too, was unable to make an impact after coming on for the starter in the 65th minute.
It was not for a shortage of chance. Most of Everton's offensive moves came through the winger and the forward, who tirelessly whipped dangerous crosses into the Tottenham penalty area.
Everton: The team head to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: The London club travel to St James' Park on late October for their fourth-round League Cup match against the Magpies.
Lena Voss is a tech enthusiast and freelance writer, passionate about demystifying complex innovations.