Kane beat three men on the counter-attack before curling home his 11th goal of the season as Spurs hit two goals in three minutes at the end of the first half, the second a close-range finish from Dele Alli.
The result moves Tottenham above Manchester United, who lost at home to Norwich, while Southampton sit 12th after six games without a victory.
Saints' five league wins this season had all come against teams in the bottom seven of the table before kick-off and Ronald Koeman will be concerned about his side's loss of form, with the relegation zone only seven points away.
The hosts were in fact the better side for much of the first half but they lacked a cutting edge with Graziano Pelle, recalled to the starting line-up here, and Sadio Mane now managing only one goal in their last 13 games combined.
Hugo Lloris, Jan Vertonghen and Toby Alderweireld - the latter prized from the clutches of Southampton when he joined Spurs from Atletico Madrid in the summer - have been integral to Tottenham's success this season and the trio played a key part again in keeping Saints at bay.
They were called into action early on as Mane twice went close in the opening 10 minutes but Alderweireld did well to block the striker's first effort before an excellent low save from Lloris denied the second.
Spurs struggled to find a foothold and their frustrations boiled over as Lloris berated his full-back Kyle Walker for not accepting a goal-kick short, and moments later fired a low pass into Eric Dier just to make his point.
Their attempts to play out from the back were made more difficult by Southampton's determined pressing and Mane broke through again, only to be thwarted this time by a sliding Vertonghen.
Tottenham had been on the back foot for much of the half but stunned Saints before the break with two quick-fire goals, the first a brilliant solo effort from Kane in the 40th minute.
It began with Erik Lamela and Alli both evading challenges on the counter-attack before Kane drove past two players, nicked the ball away from Virgil van Dijk and curled his finish into the bottom corner.
Saints were shell shocked and there was worse to come moments later when Walker's cross found Alli at the back post and as the hosts stopped for offside, he had time to take a touch and slot home.
Southampton came out with renewed intent after the restart, as Pelle tested Lloris with a curling long-range effort, but there was little to really trouble Tottenham as Koeman threw on Shane Long, Juanmi and James Ward-Prowse in the hope of turning the tide.
It was not until injury-time, however, that Saints looked like sparking a comeback as Ward-Prowse's low shot drew another strong save from Lloris but the home fans were already filtering out as Spurs held on for the points.
TWEET OF THE MATCH
Micky Hazard (?@1MickyHazard) - " Poch is doing a great job, one or two good signings and we are really pushing on COYS"
PLAYER RATINGS
Southampton
Paulo Gazzaniga: 5
Cedric: 5
Jose Fonte (c): 5
Virgil van Dijk: 5
Ryan Bertrand: 6
Victor Wanyama: 6
Steven Davis: 7
Jordy Clasie: 7
Sadio Mane: 7
Graziano Pelle: 6
Dusan Tadic: 5
Subs:
Shane Long: 5
Juanmi: 5
James Ward-Prowse: 5
Tottenham
Hugo Lloris: 8
Kyle Walker: 6
Toby Alderweireld: 8
Jan Vertonghen: 7
Ben Davies: 6
Eric Dier: 7
Dele Alli: 8
Mousa Dembele: 7
Erik Lamela: 6
Harry Kane: 8
Christian Eriksen: 7
Subs
Tom Carroll: 5
Nacer Chadli: 5
Son Heung-Min: 5
STAR PLAYER
Dele Alli
The midfielder was the busiest individual in what was a fine team performance
He, as is the case for Tottenham this season, has played better, but his influence was consistent, and when he demonstrated his composure with Spurs' second goal he also happened to secure all three points
Toby Alderweireld, incidentally, and at one of his former clubs, also impressed.
MOMENT OF THE MATCH
Sadio Mane had a fine opportunity to score in the eighth minute, when Southampton were in the ascendancy
There was little wrong with the finish, but Tottenham's Hugo Lloris produced an exceptional save to keep the score at 0-0
A lesser goalkeeper would not have done so, and the game would thereafter have been entirely different - in such moments are matches won and lost.
VIEW FROM THE BENCH
Tottenham's Mauricio Pochettino will no doubt be encouraged by another victory that suggests last week's 2-1 home defeat by Newcastle was little more than a blip
His team were clinical and ruthless as opposed to impressive, but that mattered little in what, by the final whistle, had become a routine victory.
Southampton's Ronald Koeman simply appears short of luck
He has impressed so far in England, and had organised and motivated his players to inspire what was an encouraging opening 30 minutes when all they lacked was a goal
Koeman cannot be blamed for Lloris saving from Mane.
MOAN OF THE MATCH
James Ward-Prowse was again named as a substitute
Beyond the fact it hurts the England national team that one of the most promising young English players is not getting the first-team football he deserves, when Southampton are so obviously out of form it is puzzling Ronald Koeman is continues to be reluctant to give him a chance
It was Southampton's English contingent, Ward-Prowse included, that made them such a strong team under Koeman's predecessor Mauricio Pochettino
When he did come on, he would have scored but for another excellent Lloris save - a fine talent is going to waste.
WHO'S UP NEXT
Southampton v Arsenal (Barclays Premier League, Saturday, December 26)
Tottenham v Norwich (Barclays Premier League, Saturday, December 26)
Source : PA
Source: PA