Harry Kane scored an impressive solo goal at St. Mary's stadium after beating three men on the counterattack and curling home his 11th goal of the season.
Dele Alli added a second from close range as Spurs hit two goals in three minutes at the end of the first half.
Spurs' first league win in four matches put the north London team above Manchester United, while Southampton sits 12th after six games without a victory.
Saints' five league wins this season had all come against teams in the bottom seven of the table before kickoff and Ronald Koeman will be concerned about his side's loss of form, with the relegation zone only seven points away.
Tottenham had been on the back foot for much of the first half but stunned Southampton before the break with two quick-fire goals.
It began with Erik Lamela and Alli both evading challenges on the counter-attack before Kane drove past two players, took the ball away from Virgil van Dijk and curled his finish into the bottom corner.
There was worse to come for the Saints moments later when Kyle Walker's cross found Alli at the back post and, as the hosts stopped for offside, he had time to take a touch and slot home.
Southampton came out with renewed intent after the restart, as Graziano Pelle tested Hugo Lloris with a curling long-range effort, but there was little to really trouble Tottenham.
Related story
Arsenal beats Southampton 2-0, climbs into 5th in EPL
