Kevin Mirallas fired a spectacular opening goal on Sunday to leave Tottenham staring at the prospect of a third consecutive league defeat at home.
But fears on the White Hart Lane terraces were eased by Christian Eriksen's 21st-minute equaliser before much-maligned striker Roberto Soldado scored what proved to be the winner in first-half stoppage time.
Soldado's attacking partner Kane impressed throughout and had a hand in both goals.
The England Under-21 international's tenacity in winning back possession from Gareth Barry set in motion the move for Soldado's strike - a demonstration of the high-tempo, quick-pressing style that Pochettino employed successfully during his time in charge of Southampton.
"It feels amazing to get the win. It was tough out there, Everton are a great side," Kane told Sky Sports having been named as the broadcaster's man of the match,
"It was a good battle between both teams and we're absolutely buzzing to come out with the win in the end.
"That's what we've been working on - pressing high and winning the ball high up the pitch, creating opportunities.
"We caught them on the ball and we managed to counter and get the goal.
"That's what the manager has been working on and it's good to see it working on the pitch."
Kane was a constant menace to the Everton defence during the first half, linking well with fellow Tottenham academy products Ryan Mason and Nabil Bentaleb, who took control of midfield.
"Obviously it's great to be playing with your mates who you've come up through the ranks with," Kane added.
"I think we showed we're good players. We played well, we worked hard for each other and managed to get the win so we're delighted."
