Eden Hazard opened the scoring after six minutes, before Oriol Romeu levelled proceedings midway through the first half.
Gary Cahill scored with almost the last kick of the half to regain the lead for the home side.
Diego Costa was on target at both the start and the end of the second period to secure the win. While Ryan Bertrand scored a last minute consolation for the travelling side.
The win means Tottenham Hotspur must win tomorrow to keep the pressure on Antonio Conte's men.
Saints cancel out Hazard opener
Chelsea looked like they may be feeling the jitters early on but after only six minutes, Conte's men made Southampton pay.
Maya Yoshida was dozing as Costa broke down the right. The striker rolled a pass back to Hazard, who fired low into the far corner as opposition defenders admired him.
Chelsea wasted no time in looking for their second. Victor Moses feeding Costa through on goal but his effort was well blocked for a corner.
Hazard almost added a second after 18 minutes, after beating the offside trap and being played through by Costa, the Belgian fired high and wide with a first time effort.
The Blues were having the majority of the play but Southampton managed to hit back before the half hour mark.
Steven Davis earned a corner with a deflected effort and from the set piece, Manolo Gabbiadini was found at the back post and Romeu was on hand from close range after the Italian sent the ball back across goal.
Chelsea search for the lead
With the scores back level, Chelsea began to search for the lead. N'Golo Kante burst into the penalty area, weaving past bodies but Marcos Alonso's effort was blocked on its way to goal. Costa then went down in the box looking for a penalty but the referee rightly waved play on.
Kante was then booked for an extremely late challenge on James Ward-Prowse. The Saints midfielder hit a free kick off the Chelsea wall soon after.
Sofiane Boufal hammered a shot off the side netting as Southampton continued to cause Chelsea problems from corners.
But on the stroke of half time, Chelsea were back in front. An overhit corner found Kante, who swung a cross back into the area. Alonso rose highest and Cahill threw himself at the second ball to head home, narrowly missing Costa's boot as the Spaniard attempted a scissor-kick.
Fast tempo start
The second period started with both sides putting in firm challenges. Cesc Fabregas received a booking for a sneaky foul early on.
Soon after, Chelsea doubled their advantage. A short corner which Saints didn't react quick enough to allowed Hazard and Fabregas to combine and Costa was in a good position to head home his countryman's cross.
Dusan Tadic then saw his first real action of the game. The Serb finding space outside the area and forcing Thibaut Courtois into a low save.
Chelsea were looking to kill the game when Hazard broke down the left before finding Alonso on the edge of the area. However the full back's first time shot was easily saved.
The visitors were continuing to threaten Chelsea with their set-pieces. Gabbiadini was again found at the back post from a corner but the striker fired into the side netting from a tight angle.
Seeing it out
As the game edged towards its conclusion, Southampton attempted to claw their way back into the game. Tadic forced another corner, which allowed Davis to test Courtois with a low drive.
Chelsea sprung a quick counter attack, allowing Hazard to slip Kante through on goal but Forster pulled off a fantastic save to deny the PFA Player of the Year's attempted lob.
Substitute Pedro came close to wrapping up the three points as he twisted and turned on the edge of the box before firing narrowly wide.
But that didn't matter. Two minutes later, their fourth and most fantastic goal came. Costa, played one-two's with both Hazard and then Pedro before calmly slotting past Forster.
However, in added time Southampton grabbed a consolation. Cedric Soares whipping in a ball from deep and former Chelsea man Bertand managed to rise above John Terry to score Southampton's second.
The win means Chelsea's lead at the top is back to seven points with Spurs having the luxury of a game in hand tomorrow evening.