It had all started so well for Saints, who saw Virgil van Dijk head them ahead before some fans had even taken their seats. But they allowed Alli and Kane to score with headers either side of half-time and the game was up when Nathan Redmond was sent off for fouling Alli in the box.
Kane made a complete mess of the spot-kick but made full use of the extra man to add to the score-line through substitute Son Hueng-min and Alli again. The win moved Spurs to within a point of Arsenal in fourth place in the Premier League table and left Saints where they usually are, looking on enviously in eighth.
“It’s never nice to concede so early but we didn’t panic and stuck to our gameplan. After the first goal for us it was a good game and a big statement,” said Alli.
Mauricio Pochettino, the man who left Southampton for Spurs in 2014, made a single change from the side that beat Burnley 2-1 10 days previously with Moussa Sissoko — who really should have been sent off for a wild challenge on Stephen Ward in that match — replacing Harry Winks in midfield.
Victor Wanyama made his first return since leaving Southampton for Spurs in the summer but illness prevented another Saint, Toby Alderweireld, from competing. Claude Puel, Koeman’s soft-spoken south coast replacement, made four changes from his winning side, which had triumphed 3-1 at Bournemouth.
Oriol Romeu, James Ward-Prowse, Steven Davis and skipper Jose Fonte — on the bench for the previous match amid doubts over his future — returned at the expense of Harrison Reed, Maya Yoshida, Jordie Clasie and Pierre-Emile Hojbjerg.
Saints threw everything at Tottenham in the energetic style that Pochettino brought them when he came to the south coast to replace Nigel Adkins in January 2013.
Wanyama was immediately suckered into fouling Ryan Bertrand on the left of the box and van Dijk timed his jump to perfection to head home Ward-Prowse’s free-kick with just 69 seconds on the clock.
Tottenham looked shell-shocked and rode their luck for a while, with Mousa Dembele booked for fouling Jay Rodriguez and Nathan Redmond in the space of a few seconds.
Redmond flashed a low drive just wide soon afterwards but was unfortunate to have a hand in Tottenham’s unexpected equaliser in the 19th minute.
Sissoko’s cross from the left deflected off him to give the ball extra elevation and that was just perfect for Alli to beat the static van Dijk in the air and mark his 50th Premier League game with a goal via Fraser Forster’s left-hand upright.
Confidence surged through the away ranks as a result although Fraser, who twice shanked attempted clearances, didn’t have anything else to save before the break. Twice Christian Eriksen fired off-target while in space and good defending from Fonte, sliding in at the last moment, prevented Wanyama, who had burst into the box and got the better of van Dijk, from netting a rare goal.
Kane had contributed diddly squat in the first-half but made the most of his first opportunity when it arrived. Kyle Walker used his speed to burst into the box and it took another timely intervention from Fonte to stop him. That was at the expense of a corner however and Kane, with Oriol Romeu having lost sight of him, powered a header into the top corner from Eriksen’s delivery, ending a run of 343 Premier League minutes without a goal.
Fonte headed over from a free-kick at the other end but the momentum had swung Tottenham’s way with referee Mike Dean making a pivotal decision straight after as Alli homed in on the Southampton goal.
Redmond was chasing him and clearly impeded the England man in the act of shooting, with the ball squirting wide. Dean awarded a penalty and sent the Saints man off before Kane, after a series of ludicrous little steps, blasted the spot-kick over by a considerable margin. Kane was left to scowl at the sod that moved under his feet as he struck the effort. “The ground gave way under me for the penalty, I had seen before the game that there was a new square of turf and it just gave way,” he said afterwards.
Eriksen crashed a shot against the crossbar and Danny Rose poked an effort wide as the 10 men were stretched again and again.
Lloris had been a spectator for a while but almost gifted Pierre-Emile Højbjerg, one of three 72nd-minute Saints subs, a comedy equaliser.
The Frenchman kicked the ball straight to Højbjerg, who was so surprised he sent the ball straight back instead of locating an empty net.
Son Heung-min, Tottenham’s first substitute, wrapped up victory in the 85th minute, with a cool finish across Forster after Saints had been caught on the break.
Saints couldn’t wait for the final whistle, especially after Alli strode through to slot in a fourth after the hosts had been caught out at the back once again.
Forster 5; Soares 7, Fonte 8, van Dijk 7, Bertrand 7; Ward-Prowse 7, Romeu 6, Davis 6 (Hojbjerg 72); Redmond 7, Rodriguez 5 (Long 72), Boufal 4 (Tadic 72).
Lloris 6; Walker 7, Dier 6, Vertonghen 7, Rose 7; Dembele 7, Wanyama 7; Sissoko 7 (Son 74), Alli 8, Eriksen 7; Kane 6.
Mike Dean 6