Ronald Koeman led his side to their first win at Stamford Bridge since 2002, with goals from Steven Davis, Sadio Mané and Graziano Pellè seeing the Saints come from a goal down to secure all three points.
Oriol Romeu replaced James Ward-Prowse in Koeman's starting line-up, but quickly picked up a yellow card for a trip, which led to the opening goal of the encounter.
Willian curled a free-kick from the left channel beyond Maarten Stekelenburg and inside the far post, keeping up his impressive run of scoring from set-pieces.
Virgil van Dijk was then dragged down by Branislav Ivanovic with a blatant shirt pull, but it went unpunished.
Steven Davis fired wide, before Stekelenburg pulled off two saves, first denying Eden Hazard before holding a curling effort from Oscar.
Sadio Mané then went to ground in the penalty twice in quick succession, but referee Robert Madley ignored the first challenge from Ramires, before booking Mané for simulation following a tussle with Ivanovic.
Former Portsmouth goalkeeper Asmir Begovic then denied Ryan Bertrand after he had got onto the end of a pass from Mané, before Saints eventually levelled the scores just before half-time.
José Fonte floated a free-kick forward and onto the chest of Graziano Pellè, who cushioned the ball down for Steven Davis to thump into the back of the net and draw Saints level.
It was Davis' first goal for Saints since February 2014, but it saw them go in level at the break. James Ward-Prowse came on for his 100th Saints appearance at the start of the second half, with the already-booked Romeu making way.
Mané and Dušan Tadić smartly broke an attempted offside trap from Chelsea, before Begovic came to the rescue by rushing out to save at the feet of Mané.
Falcao went to ground after breaking clear of Fonte and rounding Stekelenburg, but was rightly booked after going down too easily.
In the 60th minute, Saints finally got themselves in front, with Pellè and Tadić doubling up to make room for Mané to turn John Terry and race through on goal and poke into the net.
Saints continued to threaten, and extended their lead in the 71st minute when Pellè intercepted the ball and gave it to Mané on the half-way line, before getting it back and firing beyond Begovic from just inside the Chelsea penalty area.
There could have been a fourth goal but for a brave block from Terry to deny Tadić, but Saints left Stamford Bridge with all three points, as Chelsea's dismal start to the season continues to haunt José Mourinho.