Theo Walcott had given Everton an early lead, but doubles from Son Heung-min and Harry Kane and efforts from Dele Alli and Christian Eriksen gave Mauricio Pochettino a second successive win on the road during a week where speculation regarding his long-term future has mounted.
Spurs remain in third position but now sit just two points adrift of second-placed Manchester City, while Marco Silva's side remain in the bottom half of the standings and have now recorded just one win in seven attempts.
Everton should have opened the scoring in the 10th minute when Richarlison sent a free header wide of the target, before Kane saw a lob go marginally off target and Jordan Pickford reacted well to keep out a volley from Kieran Trippier.
An early goal appeared inevitable and it was Everton who went in front through Walcott, who converted from eight yards after Dominic Calvert-Lewin had cut the ball back from the byline.
Kane almost netted an instant equaliser with his 20-yard effort going inches over the crossbar, but Everton felt aggrieved after being denied a second goal when Calvert-Lewin was adjudged to have pushed Davinson Sanchez before heading into the far corner.
Spurs' leveller came just two minutes later. A long ball led to Pickford and Kurt Zouma getting in each other's way, and Son kept his composure to send a 25-yard effort into the far corner of an empty net.
The North London outfit remained in the ascendancy and a second goal arrived through Alli, whose half-volley was deflected into the bottom corner after Pickford had saved well from Son.
Everton needed to reach the break without conceding a third but Spurs extended their advantage through Kane, with the club's top goalscorer sending the ball into an empty net after Trippier's 25-yard set piece had hit the inside of the post.
Spurs looked like they were going to score every time they surged forward, and a fourth arrived soon after the restart as Eriksen sent a stunning volley from 20 yards into the bottom corner after Everton had only half-cleared a Kane cross.
That should have wrapped up the three points for Pochettino's men, but Everton found a way back into the game just two minutes later when Sigurdsson found the bottom corner of the net from 15 yards after being given the space to run across the edge of the area.
The goal could have acted as the catalyst for a comeback, but Spurs continued about their business in the same way and it was not long before a fifth strike was netted by the visitors.
Erik Lamela - on as a half-time substitute for Alli - powered towards the penalty area before picking out the run of Son, who controlled the pass before sending a confident finish past Pickford.
Replays suggested that Son was marginally offside, but the goal may not have had an impact on the remainder of the contest as Spurs continued to look for more goals against a struggling Everton backline.
Everton were not creating chances at the other end either, and Spurs heaped more misery on their hosts as Kane sent a first-time effort into the far corner of Pickford's net after getting on the end of Son's cross from the left.
Both teams went in search of more goals but the tally remained at eight as Spurs strolled through the closing stages to keep themselves in the title race heading into the Christmas period.
EVERTON (4-2-3-1): Pickford; Coleman, Keane, Zouma, Digne; Davies, Gomes (Schneiderlin 53'); Walcott, Sigurdsson (Tosun 83'), Richarlison (Bernard 75'); Calvert-Lewin
TOTTENHAM HOTSPUR (4-2-3-1): Lloris; Trippier, Alderweireld, Sanchez, Davies; Winks, Sissoko (Moura 83'); Eriksen, Alli (Lamela 46'), Son (Skipp 79'); Kane body check tags ::