Willian had a shot deflected on to the crossbar and Danny Ings missed a golden opportunity from close range at the other end, before Barkley created the opener for Eden Hazard.
The English midfielder pressed high to win back the ball and set up Hazard, the division's top scorer, who netted his seventh of the league season after 30 minutes at St. Mary's.
Barkley, who signed for Chelsea in January from Everton, bundled in the second with his knee from Olivier Giroud's acrobatic cross although TV replays suggested David Luiz had committed a foul in the build-up. Hazard played in substitute Alvaro Morata to seal the win in stoppage time.
Barkley's goal and assist completed a memorable few days for the midfielder, who has just been recalled to the national squad for the games against Croatia and Spain. The 24-year-old impressed at the heart of Chelsea's midfield, linking well with Jorginho and Hazard as the home side completed their ninth win in 11 games across all competitions this season.
"Ross Barkley is playing well. He scored and made an assist. He is doing well and working hard on the training ground," said Hazard.
Although Southampton should have taken a first-half lead through Ings, who blasted over from just a few yards out, they struggled to match Chelsea's pace and precision.
Ings was lucky to stay on the pitch after a wild second-half challenge on Mateo Kovacic as Southampton, who had six players booked, resorted to increasingly physical methods.
"It's too early to be thinking about the title, we know it is tough to win, But it is good to be up there. We are enjoying playing well and scoring goals. The first half was not so easy, they missed big chances and then we have had a bit of luck for our first goal, but we controlled the match in the second half,’ said Hazard.
"I don't know if I've played better (than I am now), I'm just playing good football because we are playing good football. I want to keep doing it and keep everyone happy." He added
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