Trevoh Chalobah headed in the opening goal after just nine minutes at Stamford Bridge before Romelu Lukaku and Timo Werner both had first-half finishes disallowed.
James Ward-Prowse levelled things up from the penalty spot just after the hour-mark but his day ended abruptly as he was dismissed for a dangerous challenge on Jorginho with 13 minutes left to play.
Werner proved the late hero as he sneaked in at the back post to turn home Cesar Azpilicueta’s low cross and Ben Chilwell added a late third to move the hosts two points clear at the summit.
Werner drilled the first chance of the contest into Alex McCarthy’s legs but the goalkeeper was powerless to stop the opener five minutes later.
Ruben Loftus-Cheek latched onto Chilwell’s corner to flick towards the back post where the unmarked Chalobah produced a simple diving header to score his second goal at home with just his second shot.
Ward-Prowse almost responded immediately for the visitors, but his half-volley angled narrowly wide before Theo Walcott inexplicably headed wide from point-blank range.
Lukaku then saw his left-footed strike ruled out for offside before Werner’s headed goal was overturned for Cesar Azpilicueta’s foul on Kyle Walker-Peters in the build-up.
Valentino Livramento came back to haunt his old side after the interval as he induced a foul from Chilwell to win a penalty, which Ward-Prowse duly tucked into the bottom-left corner.
Werner seemed a certainty to restore the hosts’ lead but McCarthy raced out to produce an excellent stop before Ward-Prowse was sent off – after the consultation of VAR – for a reckless tackle on Jorginho.
Chelsea eventually made their numerical advantage count as Azpilicueta found space on the right to drill across for Werner to tap-in from close range.
Chilwell then added gloss to the result after Lukaku and Azpilicueta had hit the woodwork to volley home despite the best efforts of McCarthy.
Chelsea move two points clear of the chasing pack at the top with their first win against Southampton in four attempts, albeit Liverpool face fellow contenders Manchester City on Sunday.
The visitors remain without a win from their first seven games – just the third time they have achieved the unwanted feat in their top-flight history after doing so in 1996-97 and 1998-99 – and sit in 17th on just four points.
Werner saw his first-half strike ruled out and then somehow missed when one-on-one with McCarthy as the German forward managed six shots – as many as the whole Southampton team combined.
However, his game-high fourth shot on target paid dividends for Thomas Tuchel’s men and Werner, for once, will take the plaudits ahead of record signing Lukaku.