Lee Cattermole had given bottom of the table Sunderland a shock early lead. But Emmanuel Adebayor equalised and Kane, one of the promising prodigies Sherwood championed during his time as the club's director of youth development, marked his first top-flight start by putting the hosts ahead after the break before late goals from Christian Eriksen, Adebayor and Gylfi Sigurdsson sealed the demolition.
Tottenham climb back up to sixth place with the victory, while Sunderland lie seven points from safety and even their two games in hand may not be enough to save them. Sherwood's players initially looked distracted by all the speculation about their manager's future and they fell behind in calamitous fashion in the 17th minute.
Wes Brown had already headed just wide moments earlier when Tottenham got themselves into trouble from their own throw-in. After picking up a pass from goalkeeper Hugo Lloris, Vlad Chiriches played a horrendous square pass well away from any of his team-mates and Cattermole gratefully accepted the gift to slot into the unguarded net from 25 yards.
Fortunately for Sherwood, Togo striker Adebayor was back in the starting line-up after missing three matches with a gashed heel and hamstring complaint. Adebayor led the Tottenham response and curled an effort over the bar before equalising in the 28th minute.
Eriksen drilled a low delivery across the face of goal and when Brown failed to get a clearing touch, Adebayor was on hand at close-range to deflect the ball into the net off his chest. Kane then put the north Londoners ahead in the 59th minute.
Once again Denmark playmaker Eriksen was the catalyst as he whipped a teasing cross in towards Kane, who timed his run well and stretched out a boot to poke the ball beyond Vito Mannone. Sunderland boss Gus Poyet sent on Craig Gardner and Ignacio Scocco for Cuellar and Cattermole in a bid to break Tottenham's dominance.
But man of the match Eriksen killed off the Black Cats in the 78th minute when he got the goal his superb display deserved, firing home via a slight deflection off Phil Bardsley from outside the area. With lacklustre Sunderland waving the white flag in surrender, Adebayor tapped in from Kane's pass in the 86th minute to make it four and there was still time for Sigurdsson to lash home in stoppage time.