The Potters looked like they would pay for uncharacteristically poor defending in the first half, but fought back and substitute Jerome had the final say with a thumping volley from 30 yards.
Stoke had conceded only four goals at home in the Barclays Premier League all season and boasted the best defensive record in the division, but shipped three in the first half.
Captain Ryan Shawcross and full-back Geoff Cameron were both serving one-match suspensions for picking up five yellow cards, with Matthew Upson and Ryan Shotton coming in, and the reshuffle seemed to unsettle the Potters.
Poor defending allowed Rickie Lambert to open the scoring 10 minutes in and, although Kenwyne Jones soon equalised, Jay Rodriguez was presented with Saints' second in the 24th minute.
An Andy Wilkinson own goal in the 36th minute summed up a miserable half for the hosts, but they responded in the second period and Matthew Upson pulled one back in the 67th minute.
Steven Nzonzi was sent off soon after but Stoke kept pressing and got their reward, sending Southampton back into the bottom three.
Defensive stability has been one of Stoke's key strengths and there were signs the changes would have a big effect when Southampton scored in the 10th minute.
It was the first chance of the game and would have infuriated Stoke boss Tony Pulis as none of his defenders cut out Guly Do Prado's cross and Lambert had the simple task of poking in at the back post.
The hosts should have been level inside two minutes when Nzonzi's shot was deflected to Jones in space at the back post, but somehow he skewed his shot wide.
However, the big striker made amends in the 16th minute in some style with a lovely backheel from Ryan Shotton's low cross.
Stoke looked the more likely to add to their tally at that point but they well and truly shot themselves in the foot to hand Southampton a second goal in the 24th minute.
There did not look too much danger when Lambert swung in a cross from the right but Robert Huth beat his goalkeeper to the ball and poked it against the bar, leaving Rodriguez a tap-in.
The visitors had their tails up, with Jason Puncheon causing a lot of trouble on the right, and he twisted and turned his way past Andy Wilkinson before firing in a shot that Asmir Begovic pushed behind.
Puncheon played a key part in Saints' third goal after 36 minutes, with his cross headed towards goal by Lambert before Wilkinson stabbed it over the line.
Stoke started the second half brightly, no doubt responding to a few choice words from Pulis, and Michael Kightly fired in a shot from distance that Kelvin Davis comfortably held onto.
There was a worrying moment for Pulis when Huth and Wilkinson clashed heads, drawing blood from both, but they were bandaged up and able to continue, although Huth had to change his shorts as well as his shirt.
Pulis threw on a third striker as Jerome replaced Matthew Etherington, and Stoke began to pepper the Southampton box with crosses.
It was not all about the hosts, though, and Saints really should have added a fourth in the 65th minute as they split Stoke's defence open once again.
Lambert played in Rodriguez, who was denied by a fine save from Begovic, but the ball fell to Do Prado with the goal gaping only for the striker to shoot wide.
And that miss looked very costly a minute later as Stoke pulled one back. For once Southampton failed to deal with a corner and Upson squeezed his shot under Davis, who should have done better.
The Potters then appealed vociferously for a penalty when Jose Fonte appeared clearly to handle a cross in a challenge with Jones, but referee Mark Clattenburg was unmoved.
And Stoke's hopes of getting something from the game were then dealt a real blow when Nzonzi was shown a straight red card in the 71st minute for a challenge on Jack Cork.
The midfielder caught Cork with a painful blow but it looked a harsh decision and Nzonzi was clearly unhappy as he left the pitch.
Pulis made his final change, sending on Peter Crouch for Kightly, meaning Michael Owen would have to be content with a return to the bench after two months out of the squad.
Jerome was booked for protesting that Maya Yoshida had handled in the area as the hosts desperately sought a late equaliser, and when the striker did put the ball in the net shortly after he was rightly flagged for offside.
Jerome was not to be denied, though, crashing in a tremendous shot off the underside of the bar as the clock ticked towards 90 minutes, and Stoke might even have won it but Davis kept out a Crouch header at the death.