The South Korean hit two superb solo goals in the opening 23 minutes to add to the brace he netted at Stoke earlier this month and set up Mauricio Pochettino’s men for three more points.
But despite their early domination, Spurs were forced to work hard for their win after Boro defender Ben Gibson gave his side hope by outmuscling Victor Wanyama to head his side back into the game just past the hour-mark.
Kane’s continuing absence with an ankle injury ensured the visitors started with question marks over their attacking prowess and it was Boro who bossed the opening moments in the Riverside Stadium sun, Alvaro Negredo misdirecting an early header in front of goal.
But after taking time to settle, Spurs sparked with a swift sixth-minute move which ended in Dele Alli firing a long-range effort which Victor Valdes did well to push out for a corner.
And within a minute the visitors went in front when Vincent Janssen’s neat lay-off in the box sent Son dribbling his way across the box before placing a neat finish underneath the despairing Valdes.
Spurs proceeded to attack with increasing purpose and it was no surprise when they doubled their lead in the 23rd minute with Son once again taking advantage of hesitation in the Boro defence.
Searching a sight of goal, the 24-year-old dribbled down the left side of the box, beating two defenders before turning sharply and delivering a delicious right-foot finish past the static Valdes.
Alli should have got on the scoresheet before half-time when Christian Eriksen pulled the ball back inside the box and the England midfielder, normally so sure in front of goal, side-footed well over the bar.
The one-sided action continued in the second half, Eriksen tricking his way through the back-pedalling Boro rearguard with aplomb before the move finally broke down.
Boro substitute Adama Traore gave his side fresh attacking impetus after being introduced on the hour and their renewed efforts were rewarded in the 65th minute when the hosts reduced the deficit.
Stewart Downing, who had been largely ineffectual throughout the afternoon, whipped in a free-kick from the left and Gibson beat Wanyama in the box to direct a strong header beyond the reach of Hugo Lloris.
Son came close to completing his hat-trick on 75 minutes when he was fed by substitute Erik Lamela on the right side of the Boro box but saw his shot well blocked by defender Calum Chambers.
But Spurs’ lead looked increasingly vulnerable and Jordan Rhodes was not far away two minutes later when he got his head to another deep Downing cross only for Lloris to save well down low.
Ultimately Boro came up short in their quest for an equaliser leaving boss Aitor Karanka with plenty to ponder after a third consecutive top-flight defeat.