Chelsea were desperate for this win.
After starting the season with 18 wins from 26 matches in all competitions, the Blues had won just three of their past 12 before their match with Southampton.
But they always looked better than the struggling Saints with Christopher Nkunku particularly impressing as they created numerous chances.
While the French forward starred, key man Cole Palmer continued to stutter.
Much has been written about Chelsea's top scorer, who has now gone seven matches without a goal.
He missed two glorious chances when one-on-one in the first half with one effort saved by Aaron Ramsdale and another dragged wide.