The Blues took an early lead with Axel Disasi's header, but Southampton quickly leveled the score when Joe Aribo fired in an equalizer for the hosts.
Chelsea regained control, leading 3-1 at half time before second-half goals from Cole Palmer and Jadon Sancho gave the blues a comfortable 5-1 win, adding to the misery for Russell Martin’s side.
What was already a challenging task for Southampton became even more difficult when Stephens was sent off for pulling Cucurella's hair as the hosts were about to take a corner.
Chelsea, who extended their unbeaten streak to six Premier League games, could have won by an even wider margin, hitting the woodwork three times and wasting several other chances.
Despite a tough position, with Southampton at the bottom of the table and Chelsea climbing to second above Arsenal, the result showed the clear gap in performance between the two sides.
The substitute Sancho increased the gloom among the home supporters three minutes from time as the travelling fans sang “we’ve got our Chelsea back”.