Spurs maintained their good run of form with a 2-1 victory over the Saints at home in the Premier League on Sunday afternoon.
Christian Eriksen put the North London outfit in the lead at White Hart Lane after just 14 minutes, and Dele Alli doubled the advantage in the 33rd minute.
James Ward-Prowse halved the deficit for Southampton in the opening minutes of the second half.
Kane did not feature in the match for Tottenham due to injury. The England international striker was still following the game, and although he was pleased with the win, he has admitted on Twitter that he would have preferred to play.
Tottenham are second in the Premier League table at the moment with 59 points from 28 matches. Mauricio Pochettino’s side are 10 points behind leaders and London rivals Chelsea.