First-half goals from Christian Eriksen and Dele Alli proved to be enough to close the gap on leaders Chelsea back to 10 points, despite Southampton rallying in the second half after James Ward-Prowse had pulled a goal back.
The result sees Mauricio Pochettino's side extend their club-record winning streak at home in the Premier League to 10 matches, lifting them seven points clear of fifth-placed Manchester United.
Having seen Chelsea take another step towards the Premier League title with victory over Stoke City on Saturday, Spurs knew that only a win would preserve their faint hopes of chasing the Blues down, but they were without injured top-scorer Harry Kane, who is expected to miss up to six weeks with an ankle injury.
In their nine previous games without Kane this season Spurs had won just three and scored only eight goals, but replacement striker Son Heung-min had a clear chance to put any scoring concerns to bed within three minutes when he latched on to Eriksen's defence-splitting through-ball only to be denied by an imposing save from Fraser Forster.
It was a slow start for a Southampton side who were in action for the first time in more than two weeks, and they found themselves behind after just 14 minutes when Eriksen collected the ball from Mousa Dembele before cutting inside and passing a classy finish into the bottom corner from outside the area.
That made it four goals in as many Premier League home games against Southampton for the Dane, and Spurs almost made it a quickfire double just a minute later when Alli picked up possession with his back to goal inside the box, only to fire a tame shot on the turn into the arms of Forster.
The Saints were the last visiting team to win at White Hart Lane, doing so in the corresponding fixture last May, but they were mostly limited to long-range efforts in the first half and Oriol Romeu sent one such shot narrowly wide shortly after they fell behind.
Claude Puel's side had Forster to thank for keeping them in touch in the opening 45 minutes, though, with the England international making another stunning save midway through the half when he clawed Toby Alderweireld's downward header away.
While Spurs were coping well without their main striker, Southampton's new goalscoring sensation Manolo Gabbiadini was quiet until he rippled the side-netting with a snapshot from the edge of the area shortly before the half-hour mark.
The Italian picked up an injury while going for goal, though, and was forced off with a groin strain moments later as his hopes of becoming only the third player in Premier League history to score in each of his first four games in the competition came to a premature end.
It would prove to be the start of a nightmare few minutes for Southampton, who conceded a penalty shortly afterwards when Steven Davis - a two-goal hero on his last visit to White Hart Lane - brought down Alli just inside the area.
The England international stepped up to take the spot kick himself and sent Forster the wrong way to make it 11 goals in his last 12 Premier League appearances.
Southampton felt that they should have had a penalty of their own right on the stroke of half time when Hugo Lloris could only push a swerving long-range drive from Cedric Soares into a dangerous area before Ben Davies missed his attempted clearance and caught Dusan Tadic instead.
Referee Andre Marriner turned down what few complaints there were from the Southampton players, but replays showed that Davies was perhaps fortunate to get away without punishment.
The visitors did give themselves hope of a comeback just seven minutes into the second half, though, as a rare defensive error from Alderweireld allowed the ball to run all the way through to Ward-Prowse, who tucked it home at the back post to celebrate his maiden England call-up in style.
Jack Stephens needed to make an important last-ditch block to deny Spurs an immediate response through Son, but Southampton did carry more of a threat in the second half and Lloris needed two attempts to collect a shot from Shane Long shortly before the hour mark.
The closing stages were not as comfortable for Tottenham as it looked like they may have been at half time, but the hosts did a good job of keeping the Saints at arm's length and the visitors could only muster a long-range effort from Sofiane Boufal that flew a few yards wide in the closing stages.
Indeed, it was Spurs who came closest to getting the game's fourth goal when Vincent Janssen stung the palms of Forster from a tight angle in stoppage time when he may have been better off looking for support from Alli.
In addition to their perfect 10 home league wins in a row - Tottenham's longest run since October 1987 - Spurs have now won their last 13 matches at White Hart Lane in all competitions and are unbeaten in 19 outings during their final season at the stadium.
Southampton, meanwhile, remain in mid-table heading into the international break, although they do still boast two games in hand over the teams around them.