Kamaldeen Sulemana saw a close-range volley deflected on to the post early on, before Brennan Johnson scored the first of his two goals a matter of seconds later.
Johnson’s second arrived shortly before the interval, by which time Lucas Bergvall’s set-piece goal had been ruled out following a lengthy VAR check for offside.
Saints were better in the second half, but goalkeeper Guglielmo Vicario kept out Kamaldeen and Yukinari Sugawara as the visitors pushed for a route back into the contest.
Mateus Fernandes briefly offered some hope by pulling a goal back in the 90th minute, only for Spurs to add an even later third through Mathys Tel’s stoppage-time penalty.
Ivan Jurić made three changes to his side, having come so close to a first Premier League home win in charge on Wednesday night as Crystal Palace snatched a point in stoppage time at St Mary’s.
Jurić revealed Paul Onuachu had been struggling with an ankle problem in his pre-match press conference, and the striker dropped to the bench to make way for Cameron Archer to lead the line.
Elsewhere, Flynn Downes began a two-match ban after picking up his 10th yellow card of the season in midweek, while Jack Stephens was among the substitutes as Joe Aribo and Tyler Dibling came into the side, as Saints switched from a five-man defence to a back four.
Kamaldeen Sulemana's early volley deflects off Pedro Porro and onto the post
Saints came under pressure right from the start of the game, as Spurs immediately asserted their dominance with seemingly relentless possession inside the Saints half.
Cristian Romero forced a first save from Aaron Ramsdale with a bullet header from an 11th-minute corner, before Bergvall tiptoed his way into the box but scuffed his shot.
When Saints did mount their first attack, it should have brought the opening goal. Dibling delivered a teasing cross from the right that Kamaldeen met on the volley from no more than four yards out, but the ball deflected off Pedro Porro and cannoned against the post in the blink of an eye.
With Saints still cursing their luck, Spurs pounced. Son Heung-min waited for the overlapping run of Djed Spence, whose cutback was ruthlessly dispatched by Johnson from the middle of the penalty area.
Having already kept out Romero once, Ramsdale had to do so again when the defender threw himself at Porro’s far-post cross, which the England international bravely saved with his face, leading to a break in play with the keeper still dazed.
Romero had been Spurs’ biggest attacking threat, and the Argentinian thought he’d had a hand in the hosts’ second goal when his header back across goal was steered in by Lucas Bergvall, only for VAR to intervene and rule that Romero was offside from Porro’s initial free-kick. It was a decision that took nearly five minutes to make.
Eventually the action resumed, and Spurs did not need long to score a legitimate second goal.
Saints had chances to clear the danger before James Maddison looped a header back into the danger zone and Johnson was in the right place again, this time with a more subtle touch to guide the ball into the bottom corner from virtually the same spot he already scored from earlier in the game.
Brennan Johnson adds his second goal three minutes before half time
With seven added minutes signalled, largely due to the disallowed goal, Saints did manage to force a first save from Vicario through Fernandes’s skidding shot, but it had been a half to forget.
Things might have got worse when Spence shrugged aside Dibling to go through on goal, as Ramsdale was called upon once more to parry his shot as the full-back looked to curl one inside the far post.
There was much more intensity about the visitors after the interval. Kamaldeen burst into the box, Fernandes won Saints’ first corner and Aribo saw a shot blocked, as Saints showed signs of life.
Spurs were pinned back for the first time, although that did lead to a counter-attack opportunity for Son, who was only denied by a last-ditch challenge from Jan Bednarek.
Jurić made his first changes 19 minutes into the second half, introducing Will Smallbone and Welington in place of Aribo and Manning.
Ramsdale had not been called upon for some time, but did have to be alert to make another sharp save, diving low to his left to keep out Dominic Solanke’s left-footed shot before scampering to his feet to grab the loose ball. In doing so, he grabbed it with his hand outside the penalty area on the byline, but was spared a yellow card for his indiscretion.
Kyle Walker-Peters takes on former Spurs teammate Son Heung-min
Further substitutions followed with 17 minutes to go, as Dibling and Archer departed, replaced by Sugawara and Onuachu.
Solanke went close once more, this time shooting wide, before Ross Stewart made his return from injury after six months out as a late replacement for Lesley Ugochukwu.
Saints kept pushing, and after Vicario thwarted Sugawara’s deflected effort, Fernandes found space in the box to bring down a cross from Kamaldeen and bury a left-footed strike through the keeper’s legs.
Any faint hope was quickly extinguished when Welington brought down Johnson in the box, inviting substitute Tel to complete the scoring and confirm Saints’ fate.
Tottenham Hotspur: Vicario, Porro, Romero, Davies, Spence, Bergvall (Gray 81), Bentancur (Sarr 57), Maddison (Bissouma 81), Johnson, Solanke (Tel 87), Son (c) (Odobert 57).
Subs not used: Kinsky, van de Ven, Udogie, Richarlison.
Goals: Johnson (13’, 42’), Tel (90+5’ pen).
Booked: Porro.
Southampton: Ramsdale, Walker-Peters, Harwood-Bellis, Bednarek (c), Manning (Welington 64), Ugochukwu (Stewart 83), Aribo (Smallbone 64), Dibling (Sugawara 73), Fernandes, Kamaldeen, Archer (Onuachu 73).
Subs not used: McCarthy, Bella-Kotchap, Stephens, Bree.
Goal: Fernandes (90’).
Booked: Ugochukwu.