Mauricio Pochettino’s men came into the game on the back of the midweek Carabao Cup quarter-final win over rivals Arsenal at the Emirates Stadium.
Despite going behind to former Gunners’ star Theo Walcott’s early strike on Sunday afternoon the visitors recovered in style.
Son Heung-Min equalised within six minutes, before Dele Alli and Harry Kane made it 3-1 before the half-time interval.
Christian Eriksen made it four early in the second half, only for Gylfi Sigurdsson to hand the hosts a lifeline moments later.
However, Son and Kane both grabbed their second goals of the game respectively to seal the win which gives the Spurs fans an early Christmas present and moves them to within six points of leaders Liverpool, while Everton remain down in 11th on 24 points.
Boss Marco Silva made two changes to the Everton side beaten 3-1 at Manchester City last weekend with Walcott and Tom Davies coming in for Yerry Mina and Bernard.
Spurs boss Mauricio Pochettino made four changes to the XI that defeated Burnley in the Premier League eight days ago with defender Davinson Sanchez making his comeback after two months' out injury, while Son, Harry Winks and Eriksen also came in for Danny Rose, Oliver Skipp, Erik Lamela and Lucas Moura.
Everton had the first attempt on note in the 10th minute when Sigurdsson sent Walcott away down the right and his cross was headed down and wide of the post by Richarlison.
Kane was played in at the other end by Kieran Trippier two minutes later, but the prolific forward chipped his effort over Jordan Pickford and watched as it dropped the wrong side of the upright.
There was almost a huge moment of controversy on 13 minutes when Son appeared to run the ball out of play down the left of the area before pulling it back to Trippier, but Pickford’s parrying save ensured justice was done.
It was Everton who took the lead on 21 minutes when Sigurdsson played in Dominic Calvert-Lewin down the left and he teed up Walcott to finish inside Hugo Lloris’ near post from the middle of the area.
The Toffees thought they had doubled their lead on 24 minutes when Calvert-Lewin got above Sanchez and headed in from 15 yards out, but he was harshly adjudged to have shoved the Colombian defender in the back in the process.
That decision proved vital because Spurs levelled matters just three minutes later.
Kane flicked the ball towards Son, who was in a race with Kurt Zouma for possession down the right channel, when Pickford raced out of his area and made a complete mess of an attempted clearance which gifted the South Korean the opportunity to successfully convert into the empty net from a tight angle.
Kane then curled another shot just wide, before Spurs completed the turnaround with a second goal on 35 minutes.
Moussa Sissoko played in Son down the left of the area and, while his low strike was well saved by Pickford, the ball rolled invitingly to Alli who finished with aplomb.
Kane then got the goal which his first half play had threatened on 42 minutes when he was on the spot to convert from close range after Trippier’s free-kick rebounded to him off the post.
Spurs scored a fourth with their first attack of the second half on 48 minutes when Kane’s cross was only cleared as far as Eriksen and he hit a superb half-volley into the bottom corner beyond the dive of Pickford.
The three-goal cushion lasted as many minutes as Everton pulled one back on 51 when Sigurdsson surged past three defenders on the edge of the box and then fired a low strike past Lloris, who will possibly feel he should have done better.
Any hopes of an Everton comeback were extinguished on 61 minutes when Son beat the offside trap and latched on to Erik Lamela’s through ball before putting his shot through the legs of the advancing Pickford.
It got worse for the hosts on 74 minutes when Son scampered away down the left before picking out Kane in the middle and guided a right-foot effort into the bottom far corner past Pickford.
Sigurdsson looked for his second of the afternoon on 81 minutes when he collected a pass from Lucas Digne and saw his low strike well held by Lloris after taking a slight deflection on the way through to goal.