Much of the pre-match talk had centred around the battle between Kane and opponent Romelu Lukaku as the two continued their wrestle at the top of the Golden Boot scoring charts.
And it was the former who won this contest, first beating Joel with a smart 25-yard strike before slotting past the Everton goalkeeper after the break to put Spurs in charge.
Everton rallied and Lukaku grabbed a late goal to remain on Kane's coat-tails, but Mauricio Pochettino's men took the all-important points.
Tom Collomosse was at White Hart Lane to assess Tottenham's performance...
1. Pochettino sticks with his best XI
As he did last season, Pochettino appears to have settled on an XI he will use between now and the end of the campaign – fitness permitting. When Danny Rose recovers full fitness, he will surely replace Ben Davies but the rest of the team appears set in stone. With at least two midweek matches still to come, it will be interesting to see whether Pochettino shuffles his pack but the sense is that there will be few changes. There is a risk here, though: when fringe players know they will be picked only in case of injuries to others, it is difficult to keep them sharp and motivated.
2. Home comforts
This was Tottenham’s second match in a sequence of four at White Hart Lane, and brought them a record ninth straight Premier League win at their home ground. Eric Dier suggested before the game that this run of matches could shape Spurs’ season, and he may be right. The next two matches also look winnable – the FA Cup quarter-final against Millwall on March 12, and the home clash with Southampton seven days later. Win both of those, and Tottenham will be one victory away from a major final, as well as in excellent shape for a top-four finish and a place in next season’s Champions League.
3. Ben wins the Davies derby
Ben Davies has not always found life easy in the Tottenham side, as Danny Rose’s form at left-back this season has relegated him to a back-up role. His namesake at Everton, Tom, has emerged as one of the most promising young players in the country this season. Yet it was Ben who had the better game today, making some intelligent bursts forward and ensuring Everton had little joy when they tried to attack down the right. By contrast, Tom found his direct opponent, Mousa Dembele, in irresistible mood and struggled to make an impact on the game. It was no surprise to see him replaced, by Kevin Mirallas, after 63 minutes.
4. All-round Kane
Harry Kane moved two goals clear at the top of the Premier League scorers’ charts with this double, striking two very different types of goals. The first was a 25-yard rocket that caught Joel Robles slightly flat-footed; the second a calm finish under the body of the Everton goalkeeper after Dele Alli had robbed Morgan Schneiderlin. Kane can score with his left foot, with his right foot, with his head. He can score from distance or from close-range, with powerful finishes or precise ones. He still misses good chances, though. The one-on-one with Robles, shortly after Romelu Lukaku had scored for Everton, would have given the home side a more comfortable end to the game.
5. More maturity required from Tottenham
Mauricio Pochettino bristles when it is suggested that his team lack the know-how required to win trophies. Their record under him is excellent – yet still there are signs of immaturity. In stoppage time, with Spurs 2-1 up, Alli tried a backheel when he only needed to hold possession. And when Alli appeared to have made the game safe with a third in stoppage time, Tottenham were too busy celebrating to remember to mark properly at an Everton free-kick, as Toby Alderweireld’s poor positioning allowed substitute Enner Valencia to tap home. Tottenham were far better than Everton for most of this match and should not have allowed it to become so tense.