Kane had been hoping to break Alan Shearer's 22-year record for Premier League goals scored in a calendar year and the 24-year-old did just that as he moved to 39 strikes - as well as reaching 56 efforts in all competitions - with a ruthless treble on Tuesday afternoon.
Both teams were open defensively during the first few minutes of the game, and it came as no surprise when Kane almost scored after just six minutes, with his close-range effort going wide of the near post.
Southampton were almost back on level terms within two minutes when Danny Rose's header back to Hugo Lloris went over the goalkeeper, but the Frenchman managed to get back to divert the ball onto the post before keeping the attempt out.
Kane was eager to add more goals to his tally for the year and although the forward failed with two long-range efforts, he would soon score a second, again from close range.
After Alli turned on the edge of the area, the midfielder played the ball through to Son Heung-min, who sent in a cross for Kane to net from inside the six-yard box.
There was every indication that the Saints were going to run Spurs close but the North Londoners quickly added a third through Alli, who curled the ball into the bottom corner from 20 yards for his first goal in 11 matches.
Two minutes later, Son extended his side's advantage after latching onto Alli's perfectly-weighted through-ball before drilling a shot into the bottom corner from 12 yards out.
Kane came close to completing his treble with a low shot across goal, but Southampton were able to grab a consolation in the 64th minute when Boufal's effort beat Lloris at his near post.
However, Spurs reestablished their four-goal margin just three minutes later as Alli threaded a ball through to Kane, who proceeded to clip the ball over Forster and into the net for his eighth hat-trick of 2017.
Despite the scoreline, Southampton continued to throw men forward in search of goals with Jack Stephens seeing a shot tipped wide of the post by Lloris and Jan Vertonghen clearing off the line to prevent Shane Long from ending his 10-month run without a goal.
The Saints did add a second consolation goal after the match had entered the final 10 minutes, with Tadic finding the corner of the net via Lloris's hand after the ball had only been cleared to the edge of the area.
Both teams continued to push forward during the closing stages of the contest, but the goal count remained on seven as Spurs made it four victories from their last five top-flight fixtures and Southampton extended their winless streak to seven matches.
TOTTENHAM HOTSPUR (4-2-3-1): Lloris; Aurier, Sanchez, Vertonghen, Rose; Dier, Dembele (Sissoko 54'); Eriksen, Alli (Winks 84'), Son (Lamela 76'); Kane
SOUTHAMPTON (4-3-3): Forster; Stephens, Yoshida, Hoedt, Targett (McQueen 84'); Romeu, Lemina (Tadic 63'), Hojbjerg; Boufal, Redmond (Gabbiadini (63'), Long