Match ends, Southampton 0, Chelsea 3.
Chelsea head coach Maurizio Sarri expects Ross Barkley to become "very important for the England national team" after the midfielder scored and provided an assist in the Blues' win at Southampton.
Barkley set up Chelsea's opener with a fine pass to Eden Hazard, who finished with aplomb, before netting their second himself, tapping in Olivier Giroud's acrobatic cross.
In doing so, Barkley became the first Englishman to score and assist in a Premier League game for Chelsea since Frank Lampard in December 2013.
"Today he played really well," Sarri said of Barkley. "I am really happy with him because from the beginning he has improved, day by day, week by week, match by match.
"Potentially, he is a great player because he has quality, very important qualities from the physical point of view, from the technical point of view, now he's improving from the tactical point of view.
"I think he will become very important in England and for the England national team."
Alvaro Morata scored Chelsea's third deep into injury time, chipping over oncoming home goalkeeper Alex McCarthy, after a slick passing move.
Defeat for Mark Hughes' side means they remain in 16th, and their run without a win against the Premier League's 'big six' is extended to 26 games.
Meanwhile, the Blues have now won nine of their 11 games across all competitions this season, and sit second in the Premier League after Liverpool and Manchester City shared a goalless draw.
Few believed the Chelsea squad would be able to alter their style of play to match Sarri's expectations when the Italian was appointed in July.
But in simple terms, they have flourished. And 'Sarriball' was on show for all to see in the first 15 minutes at St Mary's, as the Blues held 86% of possession.
Although Southampton did grow into the game after that opening spell, in which Willian struck the bar, they could not keep Chelsea at bay for long.
Hazard's finish was typically clinical, but Barkley should also take plaudits for the opener, as it was the former Everton man who dispossessed Pierre-Emile Hojbjerg in midfield before playing a perfectly weighted pass to the Belgian.
That assist was Barkley's first in the league since April 2017, and 12 minutes into the second half, he notched his first league goal since May 2017 by tapping in Giroud's cross.
Barkley, who was named in Gareth Southgate's latest England squad on Thursday, was substituted on 81 minutes after a fine afternoon's work, but Chelsea didn't let up and they added a third deep into injury time.
Hazard again was at the heart of it as he slid in Morata, who dinked over McCarthy to score his second in as many games, after netting the winner in Thursday's Europa League clash with Vidi.
The international break has perhaps come at a bad time for Sarri and his team, given their form, but nonetheless they will carry plenty of confidence into their next Premier League match against Manchester United on Saturday, 20 October.
This defeat means Southampton have won just one league game at St Mary's in 15 attempts, a run that extends back to November 2017.
The returning Manolo Gabbiadini twice tested Kepa Arrizabalaga from range in the first half, though their best chance of the opening 45 minutes fell to Ings.
The summer signing from Liverpool has already netted three league goals for the Saints this term, but he was unable to add to that tally after 27 minutes when he volleyed Bertrand's cross over from close range.
Southampton did threaten an equaliser following Barkley's goal, and Chelsea had Arrizabalaga to thank for two fine saves in quick succession.
The Spaniard first denied Nathan Redmond's rasping effort from range, tipping it onto the bar, before diverting Ings' powerful strike away from goal with a strong right hand.
Hughes' side have now failed to beat a top-half opponent in their last 31 attempts, a run which runs back to April 2017.
Meanwhile, Hughes' own terrible run against the Blues continues. He has lost a record 19 Premier League games against Chelsea as a manager.
Southampton manager Mark Hughes told BSports Match of the Day: "We showed Chelsea too much respect and allowed their players time and space. We needed to get closer, to force them back but we never did that.
"We had a chance at 0-0 for Danny Ings, if that goes in we get a different frame of mind. We never got any momentum. Sometimes you have to be brave and we weren't able to do that."
Chelsea boss Maurizio Sarri, speaking to BSports Match of the Day about his side's title hopes: "I think the same as I did a week ago. I think Manchester City and Liverpool are a step in front of us so we are working to cover the gap."
Chelsea's Eden Hazard on Sky Sports: "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.
"I don't know if I've played better [than I am at the minute], I'm just playing good football because we are playing good football. I want to keep doing it and keep everyone happy."
After the international break, Chelsea host Manchester United on Saturday, 20 October (12:30 BST), and Southampton travel to Bournemouth later that day (15:00 BST).
Match ends, Southampton 0, Chelsea 3.
Second Half ends, Southampton 0, Chelsea 3.
Goal! Southampton 0, Chelsea 3. Álvaro Morata (Chelsea) right footed shot from the centre of the box to the bottom left corner. Assisted by Eden Hazard with a through ball.
Attempt blocked. Marcos Alonso (Chelsea) left footed shot from the left side of the box is blocked. Assisted by Eden Hazard.
Attempt missed. Danny Ings (Southampton) left footed shot from the centre of the box is close, but misses to the right. Assisted by Mario Lemina with a cross.
Danny Ings (Southampton) is shown the yellow card for a bad foul.
Mateo Kovacic (Chelsea) wins a free kick in the defensive half.
Foul by Danny Ings (Southampton).
Mateo Kovacic (Chelsea) wins a free kick in the defensive half.
Foul by Mario Lemina (Southampton).
Foul by César Azpilicueta (Chelsea).
Ryan Bertrand (Southampton) wins a free kick in the attacking half.
Foul by Antonio Rüdiger (Chelsea).
Danny Ings (Southampton) wins a free kick in the defensive half.
Attempt saved. Antonio Rüdiger (Chelsea) with an attempt from very close range is saved in the bottom right corner. Assisted by Eden Hazard with a cross.
Corner, Chelsea. Conceded by Wesley Hoedt.
Attempt blocked. Mateo Kovacic (Chelsea) right footed shot from outside the box is blocked. Assisted by Pedro.
Attempt blocked. Ryan Bertrand (Southampton) left footed shot from outside the box is blocked.
Foul by Álvaro Morata (Chelsea).
Pierre-Emile Højbjerg (Southampton) wins a free kick in the attacking half.
Attempt missed. Wesley Hoedt (Southampton) left footed shot from the left side of the box is high and wide to the left. Assisted by Mario Lemina following a corner.
Corner, Southampton. Conceded by Kepa Arrizabalaga.
Attempt saved. Danny Ings (Southampton) right footed shot from outside the box is saved in the top right corner. Assisted by Oriol Romeu.
Delay over. They are ready to continue.
Substitution, Chelsea. Mateo Kovacic replaces Ross Barkley.
Delay in match Wesley Hoedt (Southampton) because of an injury.
Attempt saved. Álvaro Morata (Chelsea) right footed shot from the left side of the box is saved in the bottom left corner. Assisted by Eden Hazard with a through ball.
Corner, Southampton. Conceded by Kepa Arrizabalaga.
Attempt saved. Nathan Redmond (Southampton) right footed shot from outside the box is saved in the top right corner.
Substitution, Southampton. Shane Long replaces Manolo Gabbiadini.
Corner, Southampton. Conceded by Marcos Alonso.
Substitution, Chelsea. Pedro replaces Willian.
Ross Barkley (Chelsea) wins a free kick on the left wing.
Foul by Cédric Soares (Southampton).
Foul by Álvaro Morata (Chelsea).
Pierre-Emile Højbjerg (Southampton) wins a free kick in the defensive half.
Attempt blocked. Eden Hazard (Chelsea) right footed shot from outside the box is blocked. Assisted by Jorginho.
Substitution, Chelsea. Álvaro Morata replaces Olivier Giroud.
Attempt missed. Wesley Hoedt (Southampton) left footed shot from the right side of the box misses to the left.
Corner, Southampton. Conceded by Antonio Rüdiger.