The Potters went into the game having conceded only four times at home in nine previous Barclays Premier League games and on the back of victory over Liverpool but shipped three in the first 36 minutes against the Saints.
Jones briefly brought the scores level at 1-1 with a neat backheel, his third goal in four games, but it was in the second half where Stoke really showed their spirit and determination.
Matthew Upson made it 3-2 in the 67th minute and, although Steven Nzonzi was sent off shortly afterward, the hosts kept pushing and got their reward in the 90th minute when Cameron Jerome crashed a brilliant 30-yard volley in off the bar.
Jones, who is keeping Peter Crouch out of the side, said: "I think in the second half we needed to come out and show some pride, not just for ourselves, but for the fans. I think we were on a great run and we paid the price for a slow start.
"We haven't been conceding that many all season and it was a shock to the system that we started like that. Everyone picked themselves up in the second half and we came out and saved the game."