The result moves Spurs closer to Liverpool in fourth place but it was not enough to lift Southampton out of the relegation zone.
Kane’s goal was his ninth in his past five Premier League starts and he is now just a goal away from becoming the 27th member of the ‘100 Club’.
But with Mauricio Pochettino’s side piling on the pressure in the closing stages against his former club, the Argentine will consider this a missed opportunity in Spurs’ hunt for a Champions League place.
The form guide appeared to give Southampton little chance of victory but this was a spirited performance from the home side. Mauricio Pellegrino’s team had not won since November and dropped into the relegation zone this weekend.
Fans are growing impatient that none of the £75 million (85 million euros, $104 million) Liverpool paid for Virgil Van Dijk has yet been invested, with just 10 days left of the transfer window.
Abdoulaye Doucoure’s controversial last-minute equaliser for Watford denied Saints two precious points last weekend and pressure is growing on the Southampton manager, who has been the target of fans’ frustrations in recent weeks.
Fortunes could hardly be more different for Spurs, managed by former Saints boss Pochettino.
He has never lost a game at St Mary’s since leaving the south coast and his team came into this fixture unbeaten in their past five Premier League matches.
Flu struck both teams in the build-up, with Southampton missing Shane Long and Tottenham without Hugo Lloris and Christian Eriksen.
– Southampton pressing –
Southampton started brightly, pressing Tottenham in a style they themselves have become known for.
Manolo Gabbiadini, making only his second start in 14 games, almost connected with Dusan Tadic’s low cross after James Ward-Prowse had found him with an excellent long-range pass.
Tadic again showed his threat down the left when another sweeping move saw Pierre-Emile Hojbjerg almost apply the finishing touch to the Serbian’s excellent cross.
Southampton took a deserved lead in the 15th minute when Sanchez deflected past his goalkeeper Michel Vorm after being tempted by Ryan Bertrand’s low cross from the left.
Spurs almost levelled two minutes later when Ben Davies’s corner eventually dropped to Eric Dier and he shot low against the right post.
But Kane moved onto 99 in the Premier League as he headed in Davies’s next corner, beating two Southampton defenders to the ball to score from close range just 197 seconds after Sanchez’s own goal.
Both teams continued to press, making for an attractive game in appalling conditions.
Spurs were close to taking the lead with Davies again the provider, this time for Moussa Sissoko, who volleyed his cross just wide.
Jack Stephens should perhaps have put Southampton back in front but he headed over the bar after finding himself unmarked from Ward-Prowse’s excellent free-kick.
The rain relented but the intensity of the game did not in the second half. Pochettino’s side did not have things all their own way, with Southampton maintaining their high-pressure approach.
But Dele Alli saw more of the ball as the game wore on and shot low just beyond the left post after good work from Mousa Dembele.
Alli then went agonisingly close six minutes from time as Sissoko found him five yards out but Stephens managed to execute a last-ditch block.
Kane was then a whisker away from reaching the century milestone as he shot inches wide of the far post in the closing stages.
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