Scott Sinclair opened the scoring when he slotted his second penalty of the campaign in the 10th minute after Potters captain Ryan Shawcross, on his 100th top-flight appearance, made a rash challenge on Wayne Routledge.
Graham then made sure of the win with five minutes remaining as he came out on top in a challenge with Jonathan Woodgate to calmly clip home his maiden strike following his £3.5million move from Watford.
Glenn Whelan went closest for the visitors as he hit the post with a low free-kick, while Jon Walters had a volley athletically tipped onto the bar by Michel Vorm as Swansea's defence remained unbreached on home soil.
Much had been made of the clash of styles between the sides and there were eight bookings in total, with Stoke's five meaning they are set for an FA fine.
Andy Wilkinson was one of those to see yellow but was fortunate not to have been dismissed for a horrible waist-high tackle on Nathan Dyer.
Swansea were without Leon Britton after the midfielder failed to overcome a back complaint, and Graham was preferred to Leroy Lita in attack while Stoke were without Matthew Etherington, who failed a fitness test on a dead leg.
The home side got off to the ideal start when Shawcross' foul on Routledge gifted Swansea the opener in the 10th minute.
The Potters skipper felled the midfielder as he raced into the box and referee Mike Jones had no hesitation in pointing to the spot, with Sinclair slotting his penalty low to Asmir Begovic's left.
Graham then came within inches of doubling the lead as he just failed to reach a Routledge cross.
Vorm had little to do in the early stages but he was alert when called upon as he made a stunning save to deny Walters, tipping the striker's improvised volley onto the bar and over.
The visitors were finding it easy to bring Peter Crouch into the game, with diminutive Swansea midfielder Joe Allen struggling to compete with the giant striker in the air.
And some sloppy play by Swansea saw them begin to enjoy long spells in the opposition half, although two trademark long throws from Rory Delap represented their only threat.
Angel Rangel headed over at the other end after meeting Mark Gower's corner before Wilkinson was guilty of an awful tackle on Dyer five minutes before the break.
The defender's challenge was waist high and left the winger on the floor in a heap, but referee Jones somehow deemed it only worthy of a yellow card.
Pulis brought former Cardiff striker Cameron Jerome on for Delap, and the forward ought to have done better than firing weakly wide after being found by a Walters header.
Whelan exchanged shoves with Ashley Williams and then hit the woodwork with a low free-kick as the feisty nature of the contest continued.
Routledge than became the latest player to see yellow after he scythed down Jermaine Pennant.
Swansea remained a threat on the break and it took an outstanding save from Begovic to deny Sinclair his second after he had cut in from the left and got away a curling right-footed effort.
The Potters were caught out again when Allen freed Sinclair, with Pennant earning a booking for a cynical foul as the Swansea man closed in on the box.
Graham then sealed the hosts' second win of the season as the striker got a lucky ricochet off Woodgate to go on and fire beyond Begovic.