Kane had hobbled out of Spurs' FA Cup win over Millwall a week earlier, but, in his absence, Mauricio Pochettino's side edged to a 10th straight league victory on home turf with goals from Christian Eriksen and Dele Alli.
While Southampton was the last visiting team to win a top-flight game at the Lane – in the closing weeks of last season – it lost their own in-form forward, Manolo Gabbiadini, to injury after half an hour of this clash, having earlier fallen behind to Eriksen's fine strike.
Alli then tucked away a penalty to secure a comfortable half-time lead for Tottenham, but James Ward-Prowse celebrated the week of his first senior England call-up with a 52nd-minute strike to give the visitors hope.
A previously confident Spurs side faced a nervy second half and failed to reassert their dominance as Southampton sought a second goal, but the equaliser did not arrive as Claude Puel's men failed to turn their momentum into genuine chances.
Another three points consolidated second place in the table for Tottenham, 10 points behind leader Chelsea.