Sadio Mane deservedly put the Saints ahead with his close-range strike in the first half, although for all their hard work the hosts were unable to double their advantage.
Stoke grew into the game following the interval, pushing for an equaliser which never came despite their efforts.
Here, Sports Mole takes a look back at the 90 minutes of action at St Mary's.
On target: 2
On target: 1
Was the result fair?
On the balance of the 90 minutes Southampton were deserved winners despite the slender scoreline. Ronald Koeman's charges appeared to have carried over the momentum from their 8-0 thrashing of Sunderland last time out, creating numerous opportunities in the first half in particular. Graziano Pelle struck the post on a couple of occasions, and the movement of the hosts' forward trio proved too much for Stoke to handle at times.
That said, Stoke certainly grew into the game as it transpired, although they were unable to create any real openings of their own. Victor Moses's chance on 16 minutes proved to be the Potters' only shot on goal in the match, with Southampton relatively comfortable winners in the end. They certainly had to show more defensive resilience than they did seven days ago against Sunderland, but this is very much another string to add to the bow of an ever-improving Southampton side.
Whichever way you look at the statistics, this truly is a shaping up to be a season to remember for supporters of the South Coast club. The bottom line is that, after nine games of the season, Southampton are second in the Premier League table. This was supposed to be a season of transition for the club, remember, following the departure of five key men, not to mention manager Mauricio Pochettino, which left the Saints seemingly in disarray.
Well Southampton may have proved their critics wrong, but they will not stop there. On today's first-half performance there is no reason why they can't finish inside the top five, earning a European spot in the process, particularly with Mane, Pelle and Dusan Tadic - who was again fantastic this afternoon - all linking up brilliantly. Tougher tests lie ahead, of course, but both defensively and offensively, Koeman's men look to be the real deal this campaign.
Stoke City's performance
Mark Hughes can be forgiven for thinking that his side were heading for a thumping in the early stages at St Mary's, with the home side creating chance after chance. In the end the Potters can be happy with their overall showing, withholding the Saints' pressure before pushing for a goal of their own in the second 45 minutes which did not arrive.
Stoke's biggest problem this season has been consistency - or a lack of it - having now lost four, won three and drawn two of their games. This result was certainly not a shock by any stretch of the imagination, particularly after Southampton's hugely promising start to the season, yet the visitors failed to create any real problems for their opponents in attack. In fact, Fraser Forster had just the one save to make all game, which is simply not good enough. There are positives for Hughes to build on, yet improvement is needed on this showing if they are to better last season's ninth-place finish.
Sports Mole's man of the match
Sadio Mane: This award could have gone to any of Southampton's attacking players in truth, but Mane just about edges it due to his strike which proved to be the winner. Koeman opted to change his side from that victory over the Black Cats, with the Senegalese attacker brought into the starting lineup, and the decision paid off thanks to his promising movement and goal-scoring ability.
The fact that Stoke were chasing the game for the best part of an hour yet failed to muster a single shot on goal in that time is rather worrying. Phil Bardsley very nearly picked out substitute Mame Biram Diouf with a fine lofted pass, but the Senegalese missed the ball on the stretch which proved to be the Potters' best chance of the second half.
By no means Jonathan Moss's most testing afternoon, with just the occasional decision to make across the 90 minutes. Stoke felt they should have had a free kick on the edge of the box when Diouf was brought down by Nathaniel Clyne 15 minutes from time, but he waved play on with the Saints nearly adding a second at the other end.
Southampton: These two sides actually do battle once more in the week when they meet in the League Cup, but next up for Southampton in the league is a trip to face Hull City.
Stoke City: Hughes's charges came up against another of the division's in-form sides next weekend when they take on West Ham United at the Britannia Stadium.