Harry Kane grabbed the first of his brace just minutes after the restart before he grabbed his second for Spurs with an hour played. "It could have been a tough game but from the start we were really on it and deserved the win".
Allardyce, who oversaw four wins out of five to begin his tenure as Everton boss, has now failed to pick up a victory in any competition for six matches now and his team's display plumbed new depths under his tenure at Wembley.
Son was involved in Spur's fourth goal in the 81st.
Allardyce's side are now winless in their last five Premier League games and have lost their last three. At least £60m, surely.
In this photo taken by the EPA, Tottenham Hotspur's Son Heung-min (L) celebrates after scoring a goal against Everton during the English Premier League match between Tottenham Hotspur and Everton at Wembley Stadium in London on January 13, 2018.
The only other player to have done that is Jermain Defoe until yesterday.
He did not net off the bench against Swansea or over 90 minutes at home to West Ham so far this year. Everton will need similar to get anything here. All that we showed today, we must [show] in every game we play, every week. Thanks for tuning into our coverage of Spurs vs Everton.
The in-form England worldwide, who took his tally in all competitions this season to 28 goals, matched Teddy Sheringham's feat after he tapped in Son Heung-min's through ball after the restart before prodding in Eric Dier's cross on the hour mark. Although it was off target, it was turned in expertly by Son.
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All four of Tottenham's goals were as simple as they come and the scoreline could easily have been double the 4-0 scoreline it ended up as. Holgate backed off and Son's shot was turned in by Kane.
Christian Eriksen, meanwhile, one of the club's most talented assets, is set to be offered a new deal in a bid to fend off interest from clubs overseas.
Yet it was Son causing the mayhem and he had another effort hit the woodwork.
The England striker would record his second of the evening against the Blues not long after when Eric Dier picked him out with a ball from the right.
Cenk Tosun is most likely to receive a place in the starting XI as Niasse and Calvert-Lewin haven't been at their best of late.
Christian Eriksen made the result a more comfortable one when he struck past Jordan Pickford following a fine sweeping move from Son and Dele Alli.
Yet the England global Alli delivered the brilliant flick and the Danish worldwide finished calmly. "If he told you and the fans that we won't be selling, it is because he will deliver on that promise".
That means Kane will not be leaving and Spurs will fend off bids for the likes of Alli, Eriksen, Danny Rosem Toby Alderweireld etc.