Spurs scored five goals in the first half of a Premier League game for the first time, with James Maddison setting the tone by scoring inside the first minute, a blow the Saints never recovered from.
Son Heung-min and Dejan Kulusevski briskly added to Spurs' lead, scoring in the 12th and 14th minutes respectively, before Pape Sarr struck soon after against a Southampton defence that was all at sea.
Maddison compounded the hosts' misery by bending in an excellent fifth in the final minute of first-half stoppage-time, as Ange Postecoglou's team began to celebrate a much-needed return to form.
Southampton was more competitive in the second half, Mateus Fernandes finding the net only to be flagged offside, but remains bottom of the Premier League, while Tottenham moves up to 10th, just five points off the top four.
Having won just one of its past six league outings, Tottenham seemed to relish cutting loose on a night when it made history.
Postecoglou's rampant team took full advantage of some generous Southampton defending, and Saints boss Russell Martin, who had disappeared down the tunnel by the time Maddison netted Spurs' fifth, may be feeling hot under the collar.
The humbling defeat marked the end of Martin's Southampton tenure, with the club confirming shortly after full-time that he had been dismissed from his role.
Postecoglou, though, was in a position to hail his side's efforts after a difficult week for him and the club.
Postecoglou, who has been under increased scrutiny after a poor run of form, had stressed the importance of a fast start to his players and was delighted with how they delivered.
"We had 10 first-team players unavailable tonight and for the lads to come out with that much energy was outstanding," he said.
"We had to come out quickly because we knew we were going to get tired. We are asking a lot of our players.
"We've had great opportunities in the last few games early on and if we'd have taken them then you put pressure on the opposition. I said to them before the game, 'Let's be ready, let's have a fast start'.
"You just want the players to feel good and get a reward for their efforts. We can't rest or rotate and you want them to feel good.