Dele Alli is not going to win any popularity awards this Christmas but Harry Kane just might. A hat-trick here saw Tottenham’s leading scorer equal Alan Shearer’s record of 36 Premier League goals in a calendar year, and he still has Southampton to come on Boxing Day. Yet Alli is becoming the pantomime villain to his team-mate’s Prince Charming. Fresh from his ugly challenge on Kevin De Bruyne last Saturday, he was booked after just four minutes of this game for going in studs up on Charlie Taylor, and was arguably lucky still to be on the pitch when he won the penalty that put his side in front two minutes later.

The Burnley fans felt so anyway, though as Alli went to ground rather easily to win the spot-kick it was hard to know which incident they were most incensed over. The tackle on Taylor was probably not deserving of a straight red card, while the penalty question, as seems to be the case so often at the moment, was infinitely more debatable.

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Yet though Burnley will bear a sense of grievance the bottom line is that Spurs were the better side, created more chances, and thoroughly deserved to climb above their hosts in the table. But for some extremely poor finishing they might have accomplished their task earlier or more emphatically; as it was goals number 13, 14 and 15 in the league for Kane this season were enough to secure the points. If Kane had been on the end of some of the openings Spurs had passed up earlier, Shearer’s record might have been demolished before Christmas.

Kane’s first was from the spot after Alli had made the most of slight contact from Kevin Long in the area. The former referee Graham Poll was on television this past week arguing that players needed to go down for officials to award a penalty, so who is to say he was wrong? The Burnley crowd needed a little more persuading, however, and Alli was heartily booed right up to the moment he was substituted five minutes from the end. “Both decisions were tough for the referee, but I don’t think we should dwell on them,” Sean Dyche said. “Spurs were the better side and Kane was by far the best player on the pitch.”

Kane almost had a quick second goal when he rolled a shot narrowly wide from an opening created by Son Heung-min, but Moussa Sissoko was guilty of squandering a glorious chance to put Spurs further ahead midway through the first half. Breaking quickly from defending a Burnley corner, Christian Eriksen picked out Alli near halfway and his pass to put Sissoko into free space behind the Burnley backline was inspired. Unfortunately finishing is not the Frenchman’s forte and, despite having plenty of time and only Nick Pope to beat, all he could manage was a shot against the goalkeeper’s legs. Even when the ball came back to him he could not beat Pope with a second attempt. Burnley’s stand-in goalkeeper deserves credit for a notable double save, though almost any other member of the visitors’ front six would have buried one or other of the opportunities.

Statistics show Burnley are not the best at coming back from behind, and to take anything from this game they needed to create something more promising before Spurs’ superior strike power took its toll. Eriksen almost found Kane at the near post right at the start of the second half, then the Dane himself was presented with a chance on the six-yard line by Son, only to shoot tamely straight at Pope.

Spurs’ superior penetration was in evidence just before the hour when Kane and Serge Aurier engineered a marvellous opening for Son, yet with the goal at his mercy and no more than a well-directed tap-in appearing necessary the Korean blasted the ball high over the bar.

By the time Kane overhit a pass to an unmarked Eriksen in the area Spurs’ finishing prowess was actually in some doubt and Burnley had had so many let‑offs they could scarcely carry on complaining about the penalty affecting the result. It could not continue and when the normally reliable Ben Mee coughed up the ball to Sissoko in his own half the result was inevitable as soon as the midfielder knocked it into Kane’s path. Composure in front of goal is what Kane does, and he duly slotted a low shot past Pope.

The hat-trick came 10 minutes later, with another bottom corner finish from Alli’s flick after the Icelander Johann Berg Gudmundsson had lost possession in a dangerous area.

All that remained was for the home fans to get incensed all over again when Sam Vokes was penalised for barging into Hugo Lloris before heading into the net. It was not much of a barge, to be fair, and the goalkeeper probably needed to be stronger, but even Burnley must know it is not 1958 any more. If Dyche and his players intend to stay in the top half then a more legitimate goal threat would not go amiss.