Micky van de Ven Double Halts The Toffees' Run at Brand New Stadium
The Dutch defender became the initial defender to net twice in a Premier League match for Spurs since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven heads into the net twice in opening period
The home side's Jake O'Brien has goal disallowed after VAR review
Pape Matar Sarr nets third in 89th minute
This loss is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender scored twice as Tottenham extended their winning streak in away games in the Premier League and handed the Toffees their first defeat at Hill Dickinson Stadium.
Everton 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 last season.
But Tottenham's leader the Dutchman struck on two occasions from corners in the first half to place their impressive record at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - headed home a final goal to seal the victory.
Jake O'Brien believed he had levelled the tally a short while after Van de Ven's opener, glancing a powerful header past Guglielmo Vicario from an set-piece.
The Portuguese striker, meanwhile, missed a number of opportunities, while the Italian goalkeeper made a succession of fine stops to ensure the London club went five away games without defeat in the Premier League.
But the VAR stepped in, advising Craig Pawson to review the goal on the pitchside monitor and the official decided that Jack Grealish and Iliman Ndiaye were in offside positions and had interfered with the Spurs keeper.
This victory moves the manager's side up to third in the division, five points off local foes and leaders Arsenal.
The Merseyside club stay 14th and sit half a dozen points ahead of the relegation zone.
Tottenham analysis: The defender fulfils role at both ends of pitch
Following a uninspiring weekday performance in the European competition against the French side, where they managed a mere attempts on goal, the manager chose the French striker in attack instead of ex-Everton forward Richarlison.
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 wasn't needed in the final outcome.
Defender the Dutchman converted into an offensive threat to be feared.
Tottenham's first goal came from a cleverly executed corner routine, with the midfielder directing the ball back across the face of goal for an unmarked Van de Ven to score.
And Ven de Ven - filling in as skipper in Cristian Romero's absence - notched his second in added time as he rose above Jordan Pickford to head home.
Van de Ven was equally outstanding in defence, combining effectively with Kevin Danso as the duo dealt superbly with the 34 crosses sent their way by Everton.
Toffees breakdown: Everton lacking striker's instinct
The club's new home had been a fortress, but it appears the freshness may have worn off slightly and supporters headed to the gates after Sarr's third for Spurs.
The end in Everton's unbeaten home run will not be a major worry for the manager, but their striker situation will be.
Beto and Thierno Barry - the Toffees' pair of established strikers - had netted only a single goal between them before the weekend's match.
And they were failed to contribute to that poor record on a damp and dreary night on in Liverpool.
Beto's form was summed up when he opted to overhead kick a golden opportunity from near the goal, even with having room and opportunity to reposition for a simpler attempt that would have tested Vicario.
The substitute, too, was unable to influence the game after coming on for the starter 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 balls into the Spurs box.
What next for these two sides?
Everton: Moyes' men head to the Stadium of Light in the Premier League on early November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on Wednesday, 29 October for their next round League Cup tie against Newcastle.