Micky van de Ven Double Ends Everton's Run at New Home Ground
The Dutch defender became the first backline player to score two goals in a Premier League match for Spurs since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven nods into the net two times in first half
The home side's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder scores third in dying moments
This loss is Everton's first at Hill Dickinson Stadium
The Tottenham defender scored twice as Spurs extended their winning streak on the road in the Premier League and delivered the Toffees their first defeat at their new home.
The Toffees were undefeated in their last five matches at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of last season.
But Spurs captain Van de Ven pounced on two occasions from set-pieces in the opening 45 minutes to place their strong form at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - headed home a third to put the game to bed.
Jake O'Brien thought he had equalized the scores a short while after the defender's opener, glancing a powerful header past Guglielmo Vicario from an set-piece.
The Portuguese striker, in the meantime, missed a number of chances, while Vicario made a series of fine stops to guarantee Tottenham went five matches on the road without defeat in the Premier League.
But the video assistant referee stepped in, advising Craig Pawson to review the goal on the screen and the referee decided that Jack Grealish and Iliman Ndiaye were in an illegal position and had impeded with the Spurs keeper.
This victory elevates Thomas Frank's team up to third in the division, five points off north London rivals and leaders the Gunners.
Everton remain 14th and sit six points clear of the drop zone.
Tottenham analysis: The defender fulfils role at both ends of the field
Following a uninspiring midweek display in the Champions League against the French side, where they mustered a mere attempts on target, the manager chose Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The new arrival was unable to influence the game before being replaced for the substitute after an hour on the pitch, but it emerged he wasn't needed in the final outcome.
Centre-back Van de Ven converted into an offensive threat to be reckoned with.
Tottenham's first goal came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an free the defender to score.
And Ven de Ven - stepping up as captain in Cristian Romero's absence - notched his next goal in first-half stoppage time as he rose above the England keeper to nod in.
The Dutchman was equally outstanding in defence, combining effectively with his defensive colleague as the duo handled excellently with the 34 crosses thrown their way by Everton.
Toffees breakdown: Everton missing striker's instinct
The club's new home had been a happy hunting ground, but it seems the freshness may have faded somewhat and supporters flocked to the exits after the midfielder's third for Tottenham.
The break in the team's unbeaten home run won't be a massive worry for the manager, but their attacking woes are.
Beto and the other striker - the Toffees' two recognised strikers - had netted only one league goal combined before Sunday's outing.
And they were failed to contribute to that poor record on a damp and dreary night on in Liverpool.
The striker's performance was summed up when he opted to bicycle-kick a golden opportunity from near the goal, despite having room and opportunity to readjust for a simpler attempt that would have challenged Vicario.
The substitute, as well, failed to make an impact after coming on for the starter in the 65th minute.
It wasn't for a lack of opportunity. Most of the home side's attacks came through the winger and Ndiaye, who relentlessly delivered dangerous crosses into the Tottenham box.
What next for these two sides?
The Toffees: The team travel to Sunderland in the top flight on Monday, 3 November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on Wednesday, 29 October for their fourth-round League Cup match against the Magpies.