Goals by Son Heung-min and Christian Eriksen on either side of a Harry Kane double handed ninth-placed Everton their third league defeat in a row.
Everton handed a debut to new £27m man Cenk Tosun following his move from Besiktas, but it was the home side who were the first to threaten after 15 minutes when Son flicked Eriksen's wicked free kick narrowly over the crossbar with Jordan Pickford rooted to the spot.
There are not many thing Kane has failed to do for Spurs in terms of scoring - but one thing is score in five successive Premier League home games.
Spurs' second on the night, Kane equalled the record set by Sheringham for scoring the most Premier League goals for Tottenham, tapping in from Son's cross-shot despite hints of offside.
Rooney did have the ball in the back of the net midway through the half when he again linked up with his new striker partner, diverting Tosun's header into the roof of the net from close range only to see his celebrations cut short by the offside flag.
Everton manager Sam Allardyce has acknowledged Tottenham Hotspur quality ahead of the Toffees game against the Lilywhites.
Watford came back from two goals down to register a 2-2 draw with Southampton at Vicarage Road.
Everton now sit ninth in the division but they have been woeful away from home having taken just 8 points from a possible 27 on the road so far this campaign.
Eriksen added the fourth with a sublime finish nine minutes from time.
While Sam Allardyce did his utmost, through mind-numbingly boring defensive tactics, to stifle and frustrate Tottenham, Mauricio Pochettino's men were up to the test. Totenham's fist good chance fell in the 15th minute to Son, whose flicked header from a Christian Eriksen free kick delivery skimmed inches over the crossbar.
Tottenham will look to close-in on the top four with a win when they take on Everton at Wembley on Saturday evening.
With Harry Kane in town, this is an issue that Everton must address, or they run the risk of being embarrassed by the Tottenham forward.
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