Micky van de Ven Double Ends Everton's Run at New Stadium
The Dutch defender became the initial backline player to net twice in a English top-flight game for Tottenham since Jan Vertonghen in spring 2013.
Match summary
Micky Van de Ven heads home twice in first half
The home side's Jake O'Brien has goal disallowed after video check
Senegalese midfielder nets third in 89th minute
This loss is Everton's initial at their new ground
Micky van de Ven found the net twice as Spurs extended their unbeaten run in away games in the Premier League and delivered the Toffees their first defeat at Hill Dickinson Stadium.
Everton were unbeaten 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 last season.
But Tottenham's leader Van de Ven pounced twice from set-pieces in the opening 45 minutes to put their impressive record at risk, and they were failed to mount a comeback before the midfielder - set up by former Toffees attacker the Brazilian - headed home a third to seal the victory.
Jake O'Brien thought he had equalized the scores five minutes after Van de Ven's first goal, glancing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, missed a number of opportunities, while Vicario made a series of fine saves to guarantee Tottenham went five away games unbeaten in the English top flight.
But the VAR stepped in, advising the match official to check the score on the pitchside monitor and the referee ruled that Jack Grealish and the attacker were in an illegal position and had impeded with the Spurs keeper.
The win elevates the manager's team up to third in the Premier League, five points off north London rivals and table-toppers Arsenal.
The Merseyside club stay in 14th position and sit half a dozen points ahead of the drop zone.
Tottenham analysis: Van de Ven excels in role at each end of the field
Following a drab weekday performance in the European competition against Monaco, where they mustered a mere two shots on target, the manager opted for the French striker in attack instead of ex-Everton forward the Brazilian.
The new arrival was failed to make much of an impact before being substituted for the substitute after 60 minutes on the pitch, but it emerged he wasn't needed in the end.
Centre-back the Dutchman converted into an offensive threat to be feared.
Tottenham's opening strike came from a cleverly executed set-piece play, with Rodrigo Bentancur directing the ball toward the face of goal for an unmarked Van de Ven to score.
And Ven de Ven - stepping up as skipper in the Argentine's absence - added his second in first-half stoppage time as he rose above the England keeper to head home.
Van de Ven was equally outstanding in defence, partnering effectively with Kevin Danso as the duo handled excellently with the 34 crosses sent their way by Everton.
Everton analysis: Everton lacking finishing touch
The club's new home had been a fortress, but it seems the novelty may have faded somewhat and fans flocked to the gates after Sarr's third for Spurs.
The end in Everton's unbeaten home run will not be a major worry for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Everton's pair of recognised centre-forwards - had scored only a single goal combined before the weekend's match.
And they were unable to contribute to that poor record on a damp and dreary evening on in Liverpool.
The striker's performance was summed up when he opted to overhead kick a golden opportunity from near the goal, even with having space and opportunity to reposition for a more conventional shot that would have challenged Vicario.
Barry, too, failed to make an impact after replacing the starter in the second half.
It wasn't for a shortage of chance. Most of Everton's offensive moves came through Grealish and the forward, who relentlessly whipped dangerous balls into the Tottenham box.
Upcoming fixtures for both teams?
Everton: The team head to Sunderland in the Premier League on early November at 20:00 GMT.
Tottenham: The London club travel to Newcastle's ground on Wednesday, 29 October for their fourth-round Carabao Cup tie against the Magpies.