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.
Tottenham only had two shots as it eased off in the second half but racked up an xG of 2.62 overall and can take great satisfaction from a significant victory that saw it move back into the top half.