The win took Antonio Conte’s men seven points clear at the top of the standings with five games remaining, although they have now played a game more than closest title rivals Tottenham, who face Crystal Palace on Wednesday.
The Blues came out the blocks flying and took the lead within the opening five minutes, Diego Costa being played through before turning the ball across for Eden Hazard, who made no mistake to fire home.
The Saints managed to pull themselves level midway through the first-half as Oriol Romeu hammered home on the rebound after Thibaut Courtois could only parry Manolo Gabbiadini’s initial effort into the path of the forward.
However, Conte’s men would take the lead down the tunnel as Gary Cahill struck right on the stroke of half-time, heading home from close-range after Marcos Alonso delivered back across goal.
It was long after the restart that Chelsea got their third, Cesc Fabregas dinking the ball back into the box after the Saints had failed to clear initially, with Costa outmuscling his man before scoring his 50th Premier League goal.
The Blues continued bossing the game almost exclusively but would have to wait until the final two minutes of the 90 to get their fourth, although it was worth waiting for as Costa showed sublime feet to skip past half the Southampton team before arrowing his shot into the back of the net.
The Saints were able to pull back another consolation goal in the fourth minute of second-half added time as Ryan Bertrand's glossed header flew past the keeper and into the bottom corner.