Willian had given the hosts an early advantage with a free kick that curled in off the far post, but the visitors hit back to level a minute before the break as Steven Davis scored his first goal in more than 60 games.
Ronald Koeman’s men were rampant in the second half, taking the lead on the hour when Sadio Mané scored his second in as many games before turning provider to set up Graziano Pellè to wrap up the scoring.
Chelsea applied late pressure, but Saints showed their defensive qualities to seal their first win at Stamford Bridge since 2002.
Koeman made one change to the side that started last weekend's win over Swansea, with former Chelsea man Oriol Romeu coming into the side in place of James Ward-Prowse.
And the midfielder was involved in the game’s opening goal when he tripped the rampaging Eden Hazard in a wide position. Willian then stepped up to expertly curl the resultant free-kick high into the air and off the far post to give the hosts a tenth-minute lead.
Minutes later, Saints had a penalty appeal waved away after Branislav Ivanovic hauled Virgil van Dijk to the ground as the Dutchman tried to to get on the end of a Davis free-kick.
Saints continued to fight back, with Davis lashing one wide after breaking into the Blues’ area having been found in space by a good pass from Tadić.
Oscar then blazed a shot over the bar as the hosts responded, before José Fonte came to the rescue with two important interceptions in quick succession.
Hazard then saw a low drive held by Maarten Stekelenburg before the Dutchman plucked Oscar’s curling effort from the air after the Brazilian pulled clear in the Saints box.
Just after the hour, Saints were again calling for a spot-kick when Mané was tripped in the box by Ramires, but their protests again fell on deaf ears with referee Robert Madley unconvinced. Then, moments later, Mané tumbled over Ivanovic’s outstretched leg – only to be booked for simulation.
With a sense of injustice in the air, Saints were spurred on. First Gary Cahill was forced to scramble the ball behind after van Dijk had nodded Davis’s free-kick across goal, before Chelsea goalkeeper Asmir Begovic was forced into an awkward one-handed save as Victor Wanyama’s cross threatened to swerve inside the far post.
Begovic then denied former Chelsea man Ryan Bertrand from close range after the overlapping full-back had been picked out by Mané’s superb pass.
The leveller arrived a minute before the break, and it was no less than Saints deserved. Fonte’s floated free-kick was chested down by Pellè for Davis to lash home his first goal since February 2014.
Koeman made a change at the break, bringing on Ward-Prowse for his 100th Saints appearance in place of Romeu, who had been shackled by his early booking.
And the second half almost started as well as the first ended, with Tadić and Mané combining to outmanoeuvre the Blues’ offside trap only for the latter’s shot to be superbly saved by Begovic.
Tadić then turned away from fellow Serbian Ivanovic to tee up Mané, whose effort was blocked by Cahill, before Ward-Prowse sent a drive just wide.
It was the hosts’ turn to be denied a penalty on 56 minutes when Radamel Falcao pulled clear of Fonte and tumbled over the onrushing Stekelenburg, but referee Madley ruled against awarding a spot-kick and booked the Colombian for his troubles.
With an hour on the clock, Saints took the lead. Pellè and Tadić combined to play in Mané, who turned Chelsea skipper John Terry before bundling the ball under Begovic for his second goal in as many games.
The Senegalese turned provider for goal number three, breaking clear of the Chelsea defence before sliding the ball into the path of Pellè, who duly dispatched his shot across goal and inside the far post.
There could well have been a fourth goal soon afterwards as the unstoppable Mané peeled away from Cahill and squared for Tadić, whose effort was blocked for a corner by Terry.
Three was enough however for Koeman's side, who picked up their first away win of the season in style.
Chelsea: Asmir Begovic; Branislav Ivanovic, John Terry (c), Gary Cahill, Cesar Azpilicueta; Cesc Fàbregas, Ramires (Nemanja Matic 46 (Loic Remy 73)); Willian (Pedro 64), Oscar, Eden Hazard; Radamel Falcao. Unused substitutes: Jamal Blackman (GK), Kurt Zouma, Baba, Ruben Loftus-Cheek.
Goal: Willian (10)
Bookings: Ramires (43), Falcao (56)
Southampton: Maarten Stekelenburg; Cédric Soares, José Fonte (c), Virgil van Dijk, Ryan Bertrand; Victor Wanyama, Oriol Romeu (James Ward-Prowse 46), Steven Davis; Sadio Mané (Maya Yoshida 90), Dušan Tadić (Jay Rodriguez 77), Graziano Pellè. Unused substitutes: Kelvin Davis (GK), Shane Long, Cuco Martina, Juanmi.
Goals: S. Davis (44), Mané (60), Pellè (72)
Bookings: Romeu (9), Bertrand (26), Mané (34), Ward-Prowse (76), Pellè (86)
Referee: Robert Madley