Spurs have had to cope with the unwanted attention of Pochettino being linked with the Manchester United job following Jose Mourinho’s sacking some days ago.
But they showed no signs of being distracted as they roared back from a goal down at Goodison Park.
Braces from Son Heung-min and Harry Kane, with Dele Alli and Christian Eriksen also on target, did the magic, after Everton had led against the run of play through Theo Walcott.
Even a strike from former Tottenham midfielder Gylfi Sigurdsson to reduce the hosts’ deficit to 4-2 early in the second half could not spark a revival.
However, fatigue may still derail Tottenham’s bid to win a first trophy under Pochettino, with Spurs still involved in four competitions.
But with Liverpool facing Arsenal and Manchester City in top-of-the-table clashes in their next three games over the festive period, Tottenham have the opportunity to haul themselves back into it.
They can turn it into a three-way title race if they maintain the standards set at Goodison.
Kane had chipped into the side-netting and Jordan Pickford produced a fine save to deny England teammate Kieran Trippier in the early stages.
But it was Everton who struck first in a wildly-open contest when Walcott stabbed home at the near-post from Dominic Calvert-Lewin’s cross.
Marco Silva’s men could even have been 2-0 up had Calvert-Lewin not been penalised for a push on Davinson Sanchez when heading home moments later.
But Spurs looked as if they could score with almost every attack and were soon on level terms after a Pickford error, when he rushed out from his goal.
The England number one only succeeded in getting in the way of his own defender Kurt Zouma and Son took advantage with a wonderful finish from a narrow angle.
Once back on level terms, Spurs were relentless as Pickford denied Son a second but Alli charged into the box to sweep home the rebound to turn the game around.
Kane is now just one goal behind Pierre Emerick-Aubameyang in the race for the English Premier League golden boot and showed his predatory instincts to side-foot into an empty net.
This was after Trippier’s fine free-kick came back off the post three minutes before half-time.
However, there was no let-up in the game’s pace after the break as Eriksen produced a technical and perfectly-controlled volley from the penalty box edge to make it 4-1.
Three minutes later Everton’s deficit was back to two as Sigurdsson dribbled across the whole Tottenham defence before firing back across Hugo Lloris.
Yet, any hope of a fightback was extinguished just after the hour mark when Son’s fine control cushioned Erik Lamela’s pass before he finished through the legs of Pickford.
It was announced some days agao that the South Korean would go to the Asian Cup in January.
This was in spite of his already representing his country at the FIFA World Cup and Asian Games earlier this year.
And Son showed why he would be missed by his club in January once more.
An inch-perfect cross was his contribution for Kane to slide in for his second of the afternoon 16 minutes from time.
Both teams face the least rest time of any English Premier League side over the festive period with another three games to come between now and New Year’s Day.(Reuters/NAN)