The Danish midfielder slapped past Fraser Forster from outside the area - finding the bottom left corner of the net.
Dele Alli doubled the lead from the spot - after he had been felled by Steven Davis.
Kane's ankle injury had been long forgotten as the north London club continued to put pressure on Chelsea at the top of the Premier League.
Saints saw their talisman Manolo Gabbiadini hobble off with what looked like a groin problem to damage the visitors' hopes of a comeback.
Tottenham: Lloris, Walker, Dier, Alderweireld, Vertonghen, Davies, Wanyama, Dembele, Alli, Eriksen, Son.
Subs: Vorm, Trippier, Wimmer, Onomah, Sissoko, Winks, Janssen
Southampton: Forster, Cédric, Stephens, Yoshida, Bertrand, Romeu, Davis (c), Ward-Prowse, Tadić, Redmond, Gabbiadini.
Subs: Hassen, McQueen, Caceres, Hojbjerg, Long, Boufal, Rodriguez
