This is Ronald Koeman's men's third home loss of the season, with his side remaining unbeaten away from home so far in 2015-16.
Mark Hughes' Stoke took an early lead against the Saints when former Barcelona man Bojan tucked away Erik Pieters' low cross beyond 'keeper Maarten Stekelenburg to silence the boisterous home crowd.
After the opener, Southampton huffed and puffed but failed to impose their will on Stoke, having only mustered one shot on target all game with Jack Butland comfortably collecting Sadio Mane's tame effort from distance.
Dusan Tadic, in particular, was wasteful on the left wing as cross after cross was handily dealt with Stoke's giant backline.
With Stoke happy to sit back in the second half and allow Southampton to try and break them down, the drab game came to an end leaving Saints fans frustrated.
Both teams started Saturday in the top three of the Premier League form table. However, this loss sees Southampton drop to eighth, while Stoke rise to the top half of the table.