Micky van de Ven emerged as the first backline player to score two goals in a English top-flight game for Tottenham since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven nods into the net twice in opening period
Everton's Jake O'Brien has equalizer ruled after video check
Senegalese midfielder nets final goal in dying moments
This loss is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender scored twice as Tottenham extended their unbeaten run on the road in the Premier League and delivered Everton their first defeat at their new home.
Everton were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having departed their historic home behind after 133 years at the end of last season.
But Spurs captain the Dutchman struck twice from set-pieces in the opening 45 minutes to place their impressive record at risk, and they were failed to turn it around before Pape Matar Sarr - assisted by former Toffees attacker Richarlison - headed home a final goal to seal the victory.
Jake O'Brien thought he had equalized the scores five minutes after Van de Ven's opener, glancing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, missed a handful of chances, while the Italian goalkeeper made a series of excellent stops to ensure the London club went five matches on the road unbeaten in the Premier League.
But the VAR intervened, instructing the match official to check the goal on the pitchside monitor and the official ruled that Jack Grealish and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
The win moves the manager's team up to third in the division, five points off local foes and leaders Arsenal.
The Merseyside club stay in 14th position and sit six points ahead of the drop zone.
Following a drab weekday display in the European competition against Monaco, where they mustered a only attempts on goal, the manager opted for the French striker up front instead of ex-Everton forward Richarlison.
The summer signing was failed to make much of an impact before being replaced for Richarlison after 60 minutes on the pitch, but it emerged he wasn't needed in the end.
Defender the Dutchman converted into an attacking force to be reckoned with.
Tottenham's first goal came from a cleverly executed corner routine, with the midfielder heading the ball back across the face of goal for an free Van de Ven to head home.
And Ven de Ven - filling in as captain in the Argentine's unavailability - added his second in first-half stoppage time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as impressive in defence, partnering well with Kevin Danso as the pair dealt excellently with the numerous deliveries sent their way by Everton.
Everton's new home had been a fortress, but it appears the novelty may have faded slightly and fans headed to the gates after Sarr's final goal for Tottenham.
The end in the team's winning streak at home will not be a massive worry for the manager, but their striker situation will be.
Beto and Thierno Barry - the Toffees' pair of recognised strikers - had netted just one league goal combined before Sunday's outing.
And they were unable 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 close range, even with having room and time to readjust for a more conventional shot that would have challenged Vicario.
Barry, too, was unable to influence the game after coming on for the starter in the second half.
It wasn't for a shortage of chance. The majority of Everton's offensive moves came through the winger and the forward, who tirelessly delivered threatening crosses into the Spurs box.
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 Newcastle's ground on late October for their next round Carabao Cup match against Newcastle.
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