Micky van de Ven Brace Halts The Toffees' Run at New Stadium
The Dutch defender emerged as the first defender to score twice in a Premier League game for Tottenham since Jan Vertonghen in March 2013.
Match summary
The Spurs defender nods home twice in first half
Everton's defender has goal disallowed after video check
Senegalese midfielder nets final goal in dying moments
The defeat is Everton's first at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Tottenham prolonged their unbeaten run on the road in the top division and delivered the Toffees their first defeat at their new home.
The Toffees were unbeaten in their five previous fixtures at their new ground at the dockside location, having left their historic home behind after more than a century at the end of the previous campaign.
But Tottenham's leader Van de Ven struck twice from corners in the opening 45 minutes to put their strong form at risk, and they were unable to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - nodded in a third to put the game to bed.
The Everton defender thought he had levelled the tally a short while after the defender's opener, glancing a bullet header past the Spurs keeper from an set-piece.
The Portuguese striker, meanwhile, failed to convert a number of chances, while Vicario made a series of fine saves to ensure Tottenham went five away games unbeaten in the English top flight.
But the VAR stepped in, advising the match official to review the goal on the screen and the official decided that the winger and Iliman Ndiaye were in offside positions and had interfered with the Spurs keeper.
The win moves Thomas Frank's side into third place in the division, five points off north London rivals and leaders Arsenal.
Everton stay 14th and are six points ahead of the drop zone.
Spurs breakdown: Van de Ven fulfils role at each end of the field
After a drab midweek display in the Champions League against Monaco, where they managed a only two shots on target, Frank opted for Randal Kolo Muani up front instead of ex-Everton forward Richarlison.
The summer signing was unable to influence the game before being substituted for the substitute after 60 minutes on the pitch, but it emerged he proved unnecessary in the final outcome.
Defender the Dutchman converted into an attacking force to be feared.
Spurs' opening strike came from a cleverly executed set-piece play, with the midfielder heading the ball back across the face of goal for an free the defender to score.
And Ven de Ven - stepping up as skipper in Cristian Romero's absence - added his next goal in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was equally impressive in defence, partnering effectively with his defensive colleague as the duo dealt superbly with the 34 crosses thrown their way by the opposition.
Toffees breakdown: Toffees missing finishing touch
The club's new home had been a happy hunting ground, but it appears the freshness may have worn off somewhat and supporters headed to the gates after the midfielder's third for Tottenham.
The break in the team's unbeaten home run won't be a major worry for David Moyes, but their striker situation will be.
Beto and Thierno Barry - the Toffees' two established centre-forwards - had scored just one league goal combined before the weekend's match.
And they were unable to add to that poor tally on a damp and dreary evening on in Liverpool.
The striker's form was summed up when he chose to overhead kick a clear chance from near the goal, despite having space and opportunity to readjust for a more conventional shot that would have tested Vicario.
The substitute, as well, failed to make an impact after replacing Beto in the second half.
It was not for a shortage of opportunity. Most of Everton's offensive moves came through Grealish and Ndiaye, who relentlessly delivered dangerous balls into the Spurs penalty area.
Upcoming fixtures for both teams?
The Toffees: Moyes' men head to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: The London club go to Newcastle's ground on late October for their fourth-round Carabao Cup tie against Newcastle.