The Britannia Stadium outfit scored through Matthew Upson and Peter Crouch in the first half, and the score stayed like that until the final whistle.
Potters boss Tony Pulis was happy with his team’s display and feels they showed adequate energy to record the victory.
“We are pleased because Brendan (Rodgers) and the backroom staff have done a great job there,” the Welsh manager told Sky Sports.
“They play great football; they move the ball fantastically well. They work very, very hard, they are nice and compact and solid.
“I thought the lads were fantastic today with the closing down and stuff. Where they get the energy from I don’t know. That is our 43rd game of the season today.
“The thing is that you stay focused. No-one will get carried away at this football club, everybody knows about the family of this club,” he concluded.
The win sees Stoke up to 12th place in the standings, whilst Swansea slip to 14th.
By Gareth McKnight