Despite the scoreline suggesting there wasn’t much between these sides, the Potters never really caused Saints goalkeeper Fraser Forster any problems all afternoon.
Sadio Mane, who had a goal chalked off last week and given as an own goal, notched his first official Saints goal in the first half to give his side a deserved lead.
Morgan Schneiderlin could have broken the deadlock before Mane’s strike, but the Frenchman saw his close-range effort thunder against the crossbar.
Stoke made several changes in the second half, which gave them more impetus, but they rarely threatened Forster’s goal.
Ronald Koeman’s men held on for their sixth win of the season to remarkably move up to second in the table. Stoke drop to 12th after the defeat.
Mane was the only change to the side that faced Sunderland and made a lively start, with Pelle just unable to turn home his cross-shot at the far post.
Steven Davis also had an effort as Saints looked to make an early breakthrough, but it was far from one-way traffic and Fraser Forster was relieved to see a sloppy clearance deflect wide off Steven Nzonzi.
Former Southampton striker Peter Crouch directed the Frenchman’s cross over as the visitors continued to press, with Victor Moses showing good skill to wriggle past several defenders before being crowded out.
At the other end, Saints winger Mane was causing havoc and giving Phil Bardsley a torrid time.
Graziano Pelle could only direct into the side-netting when the Senegal international beat the right-back to the byline, although he made amends by denying Mane a goalscoring opportunity after the Italy international shot wide under pressure.
Tadic’s fine pass set up that chance on what was proving another impressive display for Saints, which he would have capped with another goal was it not for a fine, low save by Asmir Begovic.
The Serbian, fresh from providing a record-equalling four assists last week, then laid off for Schneiderlin, who rattled the crossbar from the edge of the box as Saints looked for an opener which arrived in the 33rd minute.
Pelle saw an impressive swivelled shot come back off the post, but Mane did brilliantly to fire home the rebound off the underside of the bar
Try as they might, Saints were unable to find a second before half-time, from which they returned strongly as Pelle again hit the woodwork with a powerful header from a Tadic cross.
Mark Hughes brought on Mame Biram Diouf for Charlie Adam in a bid to alter the dimension of the game and, while it forced Saints into more mistakes, they were struggling to create clear-cut chances.
The hosts, too, were also now struggling to break down their opponents, although were still managing to get the odd shot away.
Playmaker Tadic shook off a back complaint to swivel in the box and roll an effort wide in the 66th minute, before turning provider with a corner which Pelle could only direct across the face of goal.
It was another wasted opportunity, leaving the hosts susceptible to a late Stoke comeback.
Diouf’s introduction had given City more of an attacking threat and, after having penalty appeals waved away, he came close to latching onto a raking Bardsley cross.
It was a let-off Saints were thankful for. Defending in numbers during the closing stages, they breathed a deep sigh of relief when substitute Marko Arnautovic struck wide in stoppage time as they held out for another win.
Charlie Nicholas’ verdict
Southampton played well and I thought they deserved to win the match. In the first 25 minutes or so it was a fairly well-balanced game and Stoke were playing pretty well without being overly creative. When Southampton went in front it was a really quick finish and we didn’t really get much of a response from Stoke. They didn’t get quick service to Crouch and he didn’t have midfield runners.
If Cameron and N’Zonzi are going to be holders then they’ve got to say to Charlie Adam to get further forward. Charlie Adam hardly got a kick and he was subbed. Nothing really materialised after that.