The Blues claimed a 1-0 win but Southampton pushed the current champions to their limit at Stamford Bridge on Saturday.
It was at the stroke of half time that Chelsea broke the Saints courtesy of Alonso, but not without a sizeable contribution from Willian.
The Canarinho star's show of flair and intelligent movement on the ball has certainly gone a long way in Antonio Conte's books.
With another three points in the bag for Chelsea, here are the key points from the game:
Magical Marcos Alonso
The Spaniard was at it again as he caused all sorts of problems for the visitors in the course of the match. The left wing-back was a creative force from his wing. His rushes on the left resulted in a series of saves from the Southampton goalkeeper.
He even hit the cross bar after some nice play by Willian.
It was another link-up between the two, although from a dead-ball situation, that brought the Blues their sole goal of the game.
Chelsea were awarded a free-kick, and Alonso stepped up to curl the ball over the Southampton wall and into the net.
Clean sheet for Chelsea due to a rising star?
The Blues have been having a really hard time keeping clean sheets this term, and this might cost them, especially in the Champions League.
Their group-stage performance was hardly impressive as they have all the work to do now against FC Barcelona in the Round of 16.
The rise of Andreas Christensen, however, has helped. His performances have shown that he can be a potential long-term replacement for John Jerry.
Saints deserve some credit
The visitors might have lost the match, but they played terrifically against one the Premier League's top clubs.
The visitors were not pushovers with Nathan Redmond threatening on a couple of occasions before the break .
In the second period, the Southampton side had another decent strike, but Thibaut Courtois made a brilliant same to keep Chelsea's lead.
In the end, the Saints lost, but Chelsea didn't get out of it unbruised.