Kane had hobbled out of Tottenham's 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 were the last visiting team to win a top-flight game at the Lane – in the closing weeks of last season – they 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 leaders Chelsea, with top-four rivals Manchester City and Liverpool two and three points further back respectively.
Eriksen's fine pass created an early opportunity for Son Heung-min to open the scoring, but the forward was denied impressively by Fraser Forster after running clear of the visiting defence.
And, after 14 minutes, Eriksen showed his class again to fire Spurs in front.
Picking the ball up 25 yards from goal, the Denmark international pushed the ball onto his left foot and sent a firm strike arrowing beyond Forster into the bottom-left corner.
Chances continued to come Tottenham's way, with Alli scuffing straight at Forster, who was then required to make an instinctive, clawing stop to keep out Toby Alderweireld's header.
Southampton enjoyed some openings of their own, though, as Oriol Romeu and Gabbiadini both fizzed shots wide of the left-hand post, while Dusan Tadic was spared by an erroneous flag from the assistant referee as he lashed over the top after Ryan Bertrand had kept the ball in at the byline.
But, within seconds of Gabbiadini's withdrawal, the visitors were hit by a further blow as Alli was tripped in the area by Steven Davis and coolly converted the penalty himself.
Hugo Lloris saved well from Cedric Soares's drive in first-half stoppage-time, with Ben Davies then fortunate to avoid censure for an apparent foul on Tadic, but Southampton halved the deficit within seven minutes of the restart.
Bertrand's left-wing cross was missed by Alderweireld in the middle, but arrived at the back post for Ward-Prowse to control and lash a low finish into the net.
Son sliced wide as Tottenham went back on the offensive, while Lloris gathered Shane Long's rising strike at the other end.
The visitors kept the pressure on, but they could not forge an opening in the remainder of a scrappy half and Spurs instead came closest to another goal as Forster saved from substitute Vincent Janssen in the final minute.
Key Opta stats:
- Tottenham's 10-game winning streak at White Hart Lane is their longest run since October 1987 (14 in a row).
- The only previous top-flight season than Spurs have remained unbeaten at home was 1964-1965 (21 games, 0 defeats).
- Since he made his Premier League debut in September 2013, Christian Eriksen has scored more goals from outside the box than any other player in the competition (13).
- Dele Alli has scored in three successive league appearances at White Hart Lane for the first time in his career.
- James Ward-Prowse has scored three goals in 21 Premier League appearances this season; the same tally as he had scored in 107 Premier League appearances before 2016-2017.