Eden Hazard gave Chelsea a 30th-minute lead, finishing off a pass from Barkley for his league-leading seventh PL goal of the season.
Barkley doubled the lead 12 minutes after the break, converting from close range Olivier Giroud's volleyed cross.
Southampton almost got a goal back from long-range shots by Nathan Redmond and then Danny Ings, but on both occasions Kepa Arrizabalaga, in the Chelsea goal, came to the rescue.
Substitute Alvaro Morata, played in by Hazard, lifted the ball over Alex McCarthy in stoppage time to send Chelsea temporarily top ahead of Manchester City and Liverpool on 20 points.
Southampton are 16th with five points.
Southampton: 20 Oct v AFC Bournemouth (A)
Chelsea: 20 Oct v Man Utd (H)