Spurs had to come from behind as Man Utd's Bruno Fernandes rolled in a second-minute penalty after Anthony Martial was fouled by Davinson Sanchez.
Tanguy Ndombele equalised from close range two minutes later, before quick thinking by Kane allowed Son, who started after recovering from a hamstring injury last weekend, to apply a sublime finish on seven minutes.
On 28 minutes, Martial was sent off for an altercation with Erik Lamela, before Kane fired in from Son's pass on the half-hour.
Son turned in his second, and Spurs' fourth, eight minutes before the break.
Six minutes after half-time, Serge Aurier drilled in a fifth.
Kane converted Spurs' sixth goal from the penalty spot on 79 minutes after Paul Pogba fouled Ben Davies.
Spurs move up to fifth place on seven points, while Man Utd are 16th on three points.
Man Utd: 17 Oct v Newcastle (A)
Spurs: 18 Oct v West Ham (H)