The mostly one-sided encounter in the capital ensured a 22-point gap between Saints and 17th-place Wolves remained with just seven games to play.
Wales international Brennan Johnson opened the scoring in the 13th minute and doubled his side's lead before the break to decide the tie as a contest.
Johnson's goals sandwiched a four-minute wait to rule out Lucas Bergvall's effort for offside, after Ange Postecoglou's fume at VAR dominated the match build-up.
Mateus Fernandes pulled one back right at the end of the regulation 90 minutes but substitute Mathys Tel converted a penalty kick to conclude the game.
Despite the result, a sold-out away end enjoyed the sunshine and humour on offer, singing over the silent Spurs fans right up until the bitter last.
Ivan Juric made three changes to the team that impressed midweek in a 1-1 draw with Crystal Palace, although two were enforced by injury and suspension.
Joe Aribo and Cameron Archer replaced the banned Flynn Downes and Paul Onuachu - fit enough for the bench - while Juric also made a system change.
Club captain Jack Stephens made way for Tyler Dibling, as the Croatian matched the shape of 16th-place Spurs and under-pressure Postecoglou.
Cristian Romero was determined to relieve some of that pressure on his boss and won three headers in the Saints box in the first half alone.
His first was powerful but straight at Aaron Ramsdale, who saved and cleared well, before Saints created their only chance in a dreadful first half.
Dibling, a Spurs transfer target, dinked a lovely ball into the back-post, but the angle was too tight for Kamaldeen Sulemana to beat the goalkeeper.
The hosts opened the scoring after 13 minutes, when Johnson finished a slick move after his teammates had been granted freedom of the pitch to play.
Guglielmo Vicario lofted his goal kick into an unmarked man in the middle and Spurs forced their way down the left for Djed Spence to pull across the box.
Ramsdale then denied Romero for a second time, but did not know much about it as the Argentine's powerful effort smashed him straight in the face.
He could do nothing to stop Romero heading across the box for Bergvall to turn in but VAR stepped in after a lengthy delay to rule the goal out.
Three minutes before the interval, the Saints defence stooped to new lows on the day and allowed Johnson the chance to easily prod in from close range.
James Maddison was left free to nod a weak headed clearance back over the defensive line for the Welshman, who was more aware than his opponents.
Saints had more of the ball after the break but not much happened until Ramsdale denied Dominic Solanke low down to his left after 65 minutes.
Returning Ross Stewart was introduced as Juric's fifth and final substitution, making his first appearance since October, in the 84th minute.
After a brief welcome back to the Scotsman, the away end sang, "Championship again, ole, ole," to see out the competitive Premier League season.
But it was not done - Kamaldeen crossed for Fernandes, who found the time to control, finish and halve the deficit just as four minutes of added time were signalled.
Any desperate hope was dashed when Welington lunged in on Johnson inside the box, and Tel powered the spot kick past Ramsdale to make it 3-1.
Spurs: Vicario; Porro, Romero, Davies, Spence; Bentancur (Sarr, 57), Bergvall (Bissouma, 79), Maddison (Gray, 79); Johnson, Son (Odobert, 57), Solanke (Tel, 86).
Unused subs: Kinsky, Richarlison, Udogie, van de Ven.
Booked: Porro.
Saints: Ramsdale; Walker-Peters, Harwood-Bellis, Bednarek, Manning (Welington, 63); Ugochukwu (Stewart, 83), Aribo (Smallbone, 63), Fernandes; Dibling (Sugawara, 73), Kamaldeen, Archer (Onuachu, 73)
Unused subs: McCarthy, Stephens, Bree, Bella-Kotchap.
Booked: Ugochukwu.
Referee: Michael Salisbury.