Maurizio Sarri's team sit top of the standings ahead of Liverpool's clash with Manchester City, but Southampton remain in 16th place heading into the international break.
Chelsea started the game on the front foot and the first shot of the game saw Willian strike the top of the crossbar, although his effort from 14 yards took a huge deflection.
The Blues remained in the ascendancy with Barkley curling over the crossbar, but after being second best during the opening quarter Southampton finally offered a positive response.
Manolo Gabbiadini was denied from long range but the home side should have been ahead when Ryan Bertrand found Danny Ings all on his own at the back post, with the forward somehow volleying the ball over the crossbar from six yards out.
That miss proved costly as Chelsea went ahead on the half-hour mark. Barkley dispossessed a Southampton player before threading a pass through to Hazard, who took a touch before calmly placing the ball to the left of a helpless Alex McCarthy.
Chelsea had the better of the remaining 15 minutes of the first period, but it was Southampton who tested the goalkeeper with Gabbiadini stinging the hands of Kepa Arrizabalaga from distance.
Southampton improved at the start of the second half and should have got themselves on level terms when Bertrand was found at the back post, but the left-back sent the ball over the bar from six yards out.
Ings then saw a snap-shot from 20 yards kept out by Arrizabalaga, but just as it appeared that Chelsea would find themselves under a prolonged period of pressure, the Blues doubled their advantage.
Willian's floated free kick went to Olivier Giroud whose acrobatic volley across the box found Barkley, and the midfielder could not miss from three yards out as he finally netted his first goal in a Chelsea shirt.
That goal led to Southampton having to commit more men forward but the closest that they came to halving the deficit came 13 minutes from time as Arrizabalaga made an outstanding save to tip Nathan Redmond's 25-yard strike onto the crossbar.
Chelsea went back up the other end with Hazard creating an opportunity for substitute Morata, but the Spaniard fired his effort from 10 yards too close to McCarthy.
The striker would have been disappointed having failed to take that chance but in the final seconds of the contest, Hazard teed him up again and the former Real Madrid man made no mistake in dinking the ball over McCarthy for just his second top-flight goal of the campaign.
SOUTHAMPTON (3-4-3): McCarthy; Yoshida, Bednarek (Romeu 46'), Hoedt; Soares, Hojbjerg, Lemina, Bertrand; Redmond, Gabbiadini (Long 78'), Ings
CHELSEA (4-3-3): Arrizabalaga; Azpilicueta, Rudiger, Luiz, Alonso; Kante, Jorginho, Barkley (Kovacic 81'); Willian (Pedro 75'), Giroud (Morata 68'), Hazard