Spurs monopolised possession in the early stages, breaking through after 16 minutes when Mousa Dembele struck as poor marking from a corner enabled him to control and blast home.
Two minutes later, the home side had a second as a lovely flick from Harry Kane enabled the in-form Son Heung-Min to run on and fire in an angled shot for his eighth goal in five games.
Within three minutes of the restart it was 3-0 as Kane made space inside the area after an Alli pass before striking low to put the outcome beyond any doubt with his 20th league goal of the season, and substitute Vincent Janssen rounded off the scoring with his first Premier League goal from open play in injury time.
Everton moved into fifth place in the table -- above Manchester United, who have played three games fewer -- after scoring twice in the final 20 minutes to beat Burnley 3-1 at Goodison Park.
The visitors, still without an away league win this season, survived some early scares and could have broken through when Michael Keane met George Boyd's corner but saw Ross Barkley clear off the line.
In a dramatic start to the second half, Phil Jagielka headed Everton into the lead -- but within moments goalkeeper Joel Robles gifted them the chance to level when he raced out to challenge Sam Vokes, who was heading away from goal, and brought him down for a penalty. Vokes got to his feet to thump the visitors level.
But the keeper's blushes were spared after 72 minutes when Kevin Mirallas set up Barkley, whose shot cannoned off Ben Mee and past Tom Heaton, and within two minutes Romelu Lukaku turned away from a defender and ran through to add a third.
Crystal Palace came back from 2-0 down to secure a 2-2 draw against Leicester City at Selhurst Park.
Palace, who produced a superb performance to beat Arsenal on Monday, switched off from a long Christian Fuchs throw in the opening moments and were made to pay as Robert Huth headed in.
The Eagles were two down soon after the break when Jamie Vardy rounded off a superb counter-attack, led by Riyad Mahrez, with a curling effort into the left corner.
But less than two minutes later, Sam Allardyce's side found a way back into the match when ex-Leicester man Jeffrey Schlupp crossed low for Yohan Cabaye to thump in from 10 yards. And with 20 minutes remaining they secured a valuable point when Andros Townsend crossed and Christian Benteke struck with a header.
A late strike from Fabio Borini rescued a 2-2 draw for Sunderland against West Ham United at the Stadium of Light.
Sunderland found themselves behind after only five minutes when Andy Carroll got his attempted strike all wrong but the ball fell kindly for Andre Ayew, six yards out, to finish coolly, but the bottom side were level when Wahbi Khazri struck direct from a corner, his delivery whizzing through the crowd and in off the far post.
West Ham started the second half as brightly as they did the first and scored again when James Collins headed home a Robert Snodgrass corner.
But Sunderland salvaged a draw late on when Fabio Borini hammered home after Darren Randolph had failed to hold a long cross, and the visitors had Sam Byram sent off for a second yellow card deep into stoppage time.
Stoke ended their recent poor run in style as three high-quality goals saw off Hull City in a 3-1 home win.
The Potters started on the front foot and were rewarded after just five minutes as Marko Anautovic lashed past Eldin Jakupovic, and could have double the lead when the same player volleyed over the top after the ball had been fed to him inside the area.
Hull levelled after the break when Harry Maguire scrambled home amid chaos in the Stoke area -- but Peter Crouch was on hand to thump home a 66th-minute header from a superb Jon Walters cross.
The best was yet to come, though, as Xherdan Shaqiri took a pass from Marko Arnautovic and fired home a stunning curling 35-yard strike that hammered into the top corner.
Watford deepened Swansea's relegation fears as a first-half goal was enough to secure a 1-0 victory at Vicarage Road.
Swansea, back in the drop zone after a poor recent run, exerted early pressure against their mid-table opponents, who were grateful to Heurelho Gomes for an early save from Gylfi Sigurdsson.
Watford got going as an attacking force after 26 minutes when Troy Deeney's effort was superbly saved by Lukas Fabianski.
And they broke through three minutes before the break when Alfie Mawson gave the ball away to Etienne Capoue, whose shot was well saved by Fabianski only for him to smash home the rebound.
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