The Manchester United youngster grabbed the crucial goal with a neat finish after being set free by Salif Diao.
It marked a fine fightback for Stoke after fellow promotion chasers Saints had taken the lead, Marek Saganowski poking in Chris Baird's parried effort.
Jonathan Fortune then headed home from Liam Lawrence's corner to level before Martin had the final say to seal it.
Southampton boss George Burley:
"It was about 10 minutes before kick-off when Djamel Belmadi came in from the warm-up and said he was feeling his calf.
"Then Jermaine Wright got a bang on his thigh and he had to come off so we had lost two of our midfield players within about 15 minutes.
"But we now have two home games coming up against Cardiff and Colchester and we have to return to winning ways. We have been playing good football but at the moment we are missing an end product."
Stoke: Simonsen, Hoefkens, Fortune, Higginbotham, Griffin, Lawrence (Rooney 87), Diao, Russell, Martin (Eustace 76), Sidibe, Parkin (Paterson 67).
Subs Not Used: Zakuani, Hoult.
Booked: Parkin, Diao, Griffin.
Goals: Fortune 34, Martin 72.
Southampton: Davis, Baird, Lundekvam, Powell, Bale, Guthrie (Skacel 78), Viafara, Wright (Pele 13), Surman, Saganowski, Rasiak (Wright-Phillips 70).
Subs Not Used: Bialkowski, Best.
Booked: Powell, Viafara, Bale.
Goals: Saganowski 17.
Ref: N Swarbrick (Lancashire).