The home side scored three times in the space of six second-half minutes to move to within seven points of the league leaders Leicester City, while Man United remain fifth, four points from the Champions League positions.
Spurs were boosted by the return of Jan Vertonghen, who had missed almost three months with a serious knee injury. The Belgian replaced Kevin Wimmer at the heart of the defence, while Erik Lamela came into the XI for Son Heung-min.
As for Man United, head coach Louis van Gaal made one change from his team's 1-0 win over Everton last weekend. The alteration came at full-back as 18-year-old Timothy Fosu-Mensah replaced Italian international Matteo Darmian.
Ashley Young and Ander Herrera were both named on the bench, meanwhile, leaving Michael Carrick to skipper the team from midfield and Jesse Lingard, Juan Mata and Anthony Martial in support of lone striker Marcus Rashford, who made his 10th straight start for the Red Devils.
The visitors did not have the ideal build-up to the clash in London, however, with kickoff being put back to 4.30pm after Man United's team bus got stuck in traffic heading to the stadium. An eight-mile trip from the hotel took over two hours, which would have had an impact on both sides' preparations.
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It was the visitors that made the brighter start to events in London, with Martial causing problems to the Spurs backline. A deep free kick from Carrick found the Frenchman unmarked inside the opposition box in the eighth minute, but his effort failed to test Hugo Lloris in the home side's net.
Fosu-Mensah then tried his luck for Man United after breaking forward from right-back, but the teenager's low strike was deflected wide of the post, before the lively visitors threatened from the resulting corner.
Kane brought a wonderful save from David de Gea as Spurs managed a rare venture forward in the 18th minute, but the striker was offside inside the Man United box and it would not have counted. Danny Rose then struck one two minutes later, but the left-back's effort was always moving wide of the post.
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Christian Eriksen had a long-range strike for Spurs in the 26th minute during an even period of the match, but the Dane's effort was never troubling De Gea.
Spurs then had two golden chances to make the breakthrough, but Kane, who grew into the half, was denied by a last-ditch challenge from Fosu-Mensah after De Gea had dropped a cross, before Lamela somehow headed wide of the post from an Eriksen delivery.
A buccaneering run from Kyle Walker opened up another opportunity for the home team moments later, but Fosu-Mensah was again across to make a block as the Red Devils rode their luck at the back.
The tempo dropped in the latter stages of the first period, however, as both teams looked to tighten ahead of the interval. Indeed, the opening 45 minutes ended without producing a single shot on target.
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Van Gaal decided to introduce Young at the interval and the 30-year-old went straight to the tip of the attack, with Martial still operating down the left and Mata from the right.
De Gea was forced into action on two separate occasions in the 51st minute, first to palm away an Eriksen strike, before collecting a long-range effort from Eric Dier as Spurs turned the screw in the second period.
Kane was next to try his luck for the home side in the 55th minute, but the striker's effort was always comfortable for De Gea, who was by far the busier of the two goalkeepers in the early stages of the second period.
Lingard had a half-chance for Man United just before the hour after a smart flick from Martial, but the Englishman's low effort was always moving away from the post as it remained 0-0 in London.
Man United's best chance of the match came in the 62nd minute when Martial drove past Dier and Vertonghen before striking towards goal, but Lloris stood strong to make the save against his fellow Frenchman.
Spurs had another two opportunities in the five-minute spell that followed, but De Gea used his feet to keep out a deflected cross from Rose, before Eriksen volleyed wide of the post from a good position.
The home side made the breakthrough in the 70th minute, however, when Kane picked out a pass into Eriksen, who delivered into Alli and the teenager could not miss from close range.
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Spurs quickly found a second in the 74th minute when Toby Alderweireld headed past De Gea from a Lamela free kick and less than two minutes later, it was 3-0 when Lamela placed a low effort into the bottom corner.
Man United's defence continued to struggle as Spurs pressed forward in the latter stages, while Memphis Depay and Walker both picked up yellow cards after a clash in the 83rd minute.
Spurs will continue their title challenge away to Stoke City next Monday night, while Man United, who have seen their top-four hopes take a big hit, will travel to West Ham United for their quarter-final FA Cup replay on Wednesday.