Mauricio Pochettino's side went a goal up inside the first two minutes of the clash when Alli struck, and Kane contributed by slotting home from the penalty spot on the half-hour mark and scoring a second in the 90th minute.
Spurs remain five points off leaders Leicester City in the Premier League table, but have moved up to third place.
For Norwich, they remain in a dangerous position as they are just two points above the relegation zone.
Discover how the game unfolded in Sports Mole's text coverage below.
Evening everyone! The games just keep on coming, don't they?! There is a jam-packed schedule in the Premier League tonight as eight fixtures will be played. All of the top four are in action, and we will be focusing on one of them as Tottenham travel to Carrow Road to take on Norwich.
After losing four games on the trot, Norwich are probably not too thrilled to be facing in-form Tottenham. Alex Neil's men are hosting Spurs after suffering league defeats at the hands of Stoke City, Bournemouth and Liverpool. Prior to that miserable run, they were beaten 3-0 by Manchester City in the FA Cup. Surely things can only get better...?
As for Tottenham, well, they are flying high. They have won their last four games in all competitions and have a realistic chance of winning the Premier League title this season. Not bad for a manager who is in his second season in charge at White Hart Lane. Mauricio Pochettino's side have only lost three of their 23 league games and have stormed to victory on 11 occasions - the rest have ended in a share of the spoils. Spurs earned a 3-0 win over Norwich on Boxing Day and they will be hoping for a similar result this evening.
Norwich fans, if you were hoping to see Patrick Bamford make his debut, you will be left disappointed. There is no place for the Chelsea loanee in the squad, but January signing Timm Klose has been handed his debut in defence. Ivo Pinto and Steven Naismith, both of whom arrived at Carrow Road in January, get starting spots.
Overall, Alex Neil has made five changes to the side that were beaten by Liverpool. Alexander Tettey comes back into the side after recovering from illness, while Martin Olsson, Youssouf Mulumbu and Matt Jarvis come into the side.
As for Tottenham, Pochettino has rung the chances from the side that defeated Colchester United 4-1 in the FA Cup at the weekend. Goalkeeper Hugo Lloris comes back into the fold to captain the side, while Toby Alderweireld and Moussa Dembele have also returned to the lineup.
Dele Alli, who was rested at the weekend, comes back into the lineup, joining Christian Eriksen and Son Heung-Min in a three-man attack behind Harry Kane, who will lead the line for the visitors this evening. As expected, Kevin Wimmer has kept his place in the centre of defence due to Jan Vertonghen's injury.
We can't go much further without mentioning the transfer window. The deadline passed at 11pm last night, meaning that there will be no ins and outs for Premier League teams until the summer. So, how did Norwich get on? They brought in eight new faces, including Patrick Bamford, Steven Naismith, Timm Klose, Ivo Pinto, Matt Jarvis, Ebou Adams, Ben Godfrey and James Maddison. In total, they spent just under £22m and the £8.5m that they parted with for Naismith has already looked like a bargain as he scored on his debut against Liverpool almost a fortnight ago.
The interesting acquisition is that of Bamford, who has joined on loan from Chelsea until the end of the season. The 22-year-old impressed on loan at Middlesbrough in the 2014-15 season by scoring 19 goals in the Championship, but he lost his momentum when he went to Crystal Palace at the start of this season. The forward was rarely used, making just six Premier League appearances for Alan Pardew's side, eventually resulting in him returning to Chelsea. Now, though, Bamford has a fresh chance at Norwich, where he will be hoping for more minutes on the pitch, but the forward misses out tonight.
What about Tottenham? Well, they only recruited one new face last month and that was Shilow Tracey from Ebbsfleet United for an undisclosed fee. As we know, they were by no means big spenders in the winter window, but in truth, they didn't really need to be. Pochettino's young team are having a great season and January is always a tricky window for business. The main objective for Spurs was to keep their best players, namely Harry Kane, and they were able to do just that. Manchester United and Real Madrid have been linked with moves for the prolific striker, but so far, Kane has not been swayed.
Right, back to matters at hand. Tottenham are only five points off the top spot, so a title charge must be at the forefront of the team's mind no matter how unlikely that feat may have seemed at the start of the season. Leicester City are currently leading the way (yes, really!) but with Tottenham's next two games being against Norwich and Watford, they could be right in the hunt. In fact, depending on results tonight, the North London outfit could be two points within the title if they beat Norwich.
Pochettino's squad have the youngest average age in the Premier League and it is a very attacking one as Spurs have had the most shots on target from outside of the box in the top flight this season - 53. They're not afraid to go for goal as they have actually attempted the most shots on target overall (153). At the moment, Tottenham have the joint-best goal difference in the league and considering how topsy-turvy this campaign has been, it could end up being tight at the top, therefore making goal difference all the more important.
When speaking of individual players, Harry Kane must be mentioned. The striker has found the back of the net 32 times in his last 46 league fixtures, which is only 10 fewer than Norwich as an entire team in that many games!
Another player who we must discuss is Dele Alli. Twelve months ago, the 19-year-old was playing for MK Dons and now, the teenager is arguably the most in-form player of England's elite league. The midfielder has scored six goals and made five assists so far this season and he has provided a new attacking element for Pochettino. The most recent Premier League goal was in Spurs' 3-1 triumph over Crystal Palace at Selhurst Park. Kane and Nacer Chadli also scored, but Alli stole the show with this strike...
Ahead of tonight's game, Pochettino told said: "Our mentality is good. We are ready to compete Tuesday and Saturday [against Watford], again. The spirit in the squad is fantastic. We need to keep the momentum and try to win the next game.
"I believe in my players and the squad we have to fight in every game. We know Norwich is a team that had 10 days to prepare for our game, but our mentality is good, we are strong and we need to compete."
It's not all good news for Spurs, though, as they will be without defender Jan Vertonghen for a lengthy spell because of knee ligament damage. At this stage of the season, if you're in the title race, you need all of your best players available, particularly ones who can keep out opponents! Kevin Wimmer has been deputising for Vertonghen and he will be tested tonight and in the coming weeks as he helps to keep Tottenham in the hunt for the elusive Premier League crown.
Right, let's turn our attention to tonight's host's. Norwich looked relatively comfortable towards the end of 2015 as they won three in five league matches, suffering just the one defeat. However, after suffering three league defeats on the bounce, the Canaries are staring at the exit door once again.
It is always a scrap at the bottom and at the moment Norwich are just two points from the bottom three, which is currently occupied by Newcastle United, Sunderland and Aston Villa. Unfortunately for Villa, their doomed fate looks sealed, but bitter rivals Sunderland and Newcastle are four and two points off safety respectively.
The positive aspect for Norwich is that they have had over a week to get ready for this game as they were not in FA Cup action at the weekend - a 3-0 defeat to Manchester City made sure of that. The negative aspect is that their last game was riddled with defensive errors. The match ended in a 5-4 win for Liverpool and was arguably one of the most baffling games of the season so far.
Norwich went 3-1 in front, with new boy Steven Naismith among the scorers, after coming from behind, but they were pegged back 4-3 until Sebastien Bassong struck what he and the rest of the Canaries thought was a crucial equaliser in the 92nd minute. It was not to be though, as Adam Lallana scored in the dying second of the match to give Liverpool all three points. To drop a lead like that is something that Neil will certainly not want to happen again, and given the calibre of opposition this evening, they will need to be a lot tighter at the back.
Defence has been a big problem for Norwich this season has they have the second-worst defence in the Premier League having conceded 43 goals and only keeping three clean sheets in 23 games. The upside is that there has only been one occasions this season when Norwich have failed to score a league goal on home turf.
Neil certainly thinks that Spurs are contenders for the title and this may actually be their best chance of taking the much-coveted crown this season due to the poor form of Manchester United and Chelsea. Added to that, Pep Guardiola will be arriving at Manchester City next season and given that the Spanish coach has won 19 trophies in eight years, you have to think that only something special will be capable of beating his side to the title.
HEAD TO HEAD: As we mentioned earlier, Spurs earned a 3-0 win over Norwich at White Hart Lane on Boxing Day, with Kane netting twice. Tottenham have a better record in past meetings between the two sides as they have won eight and lost there of their 15 Premier League matches against the Canaries. In addition, Norwich have scored just five goals in their last 11 top-flight games against Tottenham.
PREDICTION: Right, how do you see this one turning out? Spurs are the overwhelming favourites to get a result and you can't really dispute that. They have already picked off the Canaries this season and considering that Norwich have conceded more goals from opposition counter attacks than any other team in the Premier League, this could end up being a routine win for Pochettino's men.
What a start for Tottenham! Dele Alli scores his seventh goal of the season! The move began from a corner which Norwich struggled to clear. The ball eventually fell to Walker, whose shot is blocked and deflected into Eriksen's feet. The Dane tries to shoot the ball into the far corner, but the keeper stops. The ball only falls as far to Alli, who stabs it home.
Great defending from Walker! Norwich try to respond by sending the ball over the top looking for Naismith, who would have been through on goal had it not been for Walker. The defender manages to get in front of the forward to knock the ball out for a corner, which comes to nothing.
Norwich have shown their defensive frailties early in this game and they quickly need to recover. The Canaries cannot afford to be caught napping against this calibre of opposition, particularly against a goal-hungry Alli!
Son shows quick feet on the right-hand side after collecting the ball from walker. He creates half a yard of space for himself before launching a shot from outside of the box, but it soars over the crossbar and into the stands.
Boos ring around the stadium as Tottenham get a free kick in the middle of the park following a foul from Tettey. Referee Kevin Friend has a word with the Norwich player as opposed to reaching for a card. The home side's frustrations are showing.
The diagonal ball comes in searching for Alli, who gets a nudge in the back from Pinto and goes to ground as a result. The referee doesn't blow for a foul and in fairness to Pinto, it would have been harsh to penalise him.
A huge call from the referee! Spurs are given a penalty after Bassong clips Alli when the midfielder goes for the rebound off Kane's shot. There aren't many calls for it from Spurs, but not many complaints from Bassong either.
OFF THE POST! A brilliant first touch from Kane as he collects the ball before charging into the box on the left side. He unleashes a shot with his left foot at a tight angle, but it clatters off the frame of the goal.
CHANCE! Alli is left with his head in his hands after missing a free header. The ball is whipped in and the midfielder has plenty of time to trouble the keeper, but his attempt bounces out for a goal kick.
It's plain sailing for Tottenham as they enter the half-time break two goals to the good at Carrow Road. Dele Alli gave the visitors a perfect start when he slotted home inside the first two minutes of the game. Norwich struggled to respond and their defensive frailties showed. Spurs punished their opponents further when Harry Kane scored from the spot kick after Alli was awarded a penalty after being brought down by Sebastien Bassong in the box. Norwich have plenty to do! We'll return for the second half shortly.
The home side have found some fight from somewhere as they are closing down the Spurs players much more than they were in the first half. There is plenty more aggression in their game in these early stages, but they will need to turn that into goals if they want to get anything out of this game.
CHANCE! Spurs show that they're not sitting back on their lead just yet. Kane latches onto the ball after Klose fails to control a throw-in from Pinto. The striker darts down the left before unleashes a shot, but it drags wide.
Norwich get the ball in the net for the second time of the game, but it's disallowed once again! Bassong is the man who gets a touch on the ball after Naismith latched on in the penalty area, but Bassong is offside.
Norwich are definitely the team on top at the moment, but they will be kicking themselves for not starting like this in the first half! Jarvis has been getting more involved as the game has gone on, sending some decent crosses into the box.
CHANCE! Oh Naismith, you should have done much better there! The striker gets the ball off Mbokani before going for glory. He had plenty of options either side, but he chose to ignore them and his attempt flew wide.
There we have it! It was a comprehensive win for Tottenham as they rarely looked troubled at Carrow Road. Dele Alli opened the scoring in the second minute and Harry Kane punished Norwich further by scoring from the penalty spot on the half-hour mark. The Canaries came to life in the second half, but their surge failed to make an impact as Kane wrapped up the win with a goal in the 90th minute.
Spurs remain in the hunt for the title as they are still five points off leaders Leicester and they have moved up to third in the table. For Norwich, they still have some work to do as they are just two points above relegation. Thank you for joining us and until next time, goodbye!
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