The Swans made one change to the starting line-up as Neil Taylor returned at left-back after serving a two-match ban, replacing the injured Jordi Amat (foot).
There was a first appearance on the bench for 21-year-old left-back Raheem Hanley, who was promoted from the club's Under-21s set-up.
Garry Monk was also without Kyle Bartley (knee), while Bafe Gomis (hamstring) and ankle victims Kyle Naughton, Tom Carroll and Wayne Routledge all remained on the injury list.
SWANS: Lukasz Fabianski, Angel Rangel, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Jack Cork, Jonjo Shelvey, Gylfi Sigurdsson, Nathan Dyer (Ki Sung-Yueng, 77), Jefferson Montero (Modou Barrow, 87), Nelson Oliveira (Marvin Emnes, 41).
SUBS: Gerhard Tremmel, Raheem Hanley, Leon Britton, Matt Grimes.
STOKE CITY: Jack Butland, Phil Bardsley, Erik Pieters, Glenn Whelan, Marko Arnautovic, Marc Wilson, Steven N'Zonzi, Charlie Adam (Stephen Ireland, 70), Ryan Shawcross (capt), Mame Biraf Diuof (Peter Crouch, 80), Jonathan Walters (Peter Odemwingie, 80).
SUBS: Thomas Sorensen, Marc Muniesa, Steve Sidwell, Philipp Wollscheid.
The Swans came into this game just one place and three points ahead of Stoke, who won the reverse fixture 2-1 at the Britannia Stadium back in October.
And with these two sides harbouring hopes of finishing eighth in the Barclays Premier League, it was a typically cagey opening at the Liberty as both teams looked to give little away early on.
Nelson Oliveira - who scored his first Swans goal in the win over Newcastle last week - saw a header deflect wide before Jefferson Montero picked out the on-loan striker with a chipped ball to the far post but his scuffed volley drifted harmlessly over the bar.
The game's best chance didn't arrive until eight minutes before the break as a scuffed effort from Gylfi Sigurdsson found its way to Jonjo Shelvey, who was flagged offside despite forcing Jack Butland into a fine one-handed save low down to his right.
But the Swans were dealt a blow as Nelson Oliveira picked up a knock in the build up, with the Portuguese striker having to be replaced by Marvin Emnes.
Charlie Adam and Jonjo Shelvey both traded efforts at either end before Steven Nzonzi saw a wonderful curling effort superbly tipped away by Lukasz Fabianski in the final action of the first half.
Half-time: Swans 0 Stoke 0
Neither side made any changes at the break, but it was the Swans who made a bright start to the second half with two clear cut chances inside six minutes.
Gylfi Sigurdsson saw a fine effort come back off the top of the bar from the edge of the box before the same player somehow headed wide from six yards out after a good run and cross from Nathan Dyer.
The hosts continued to press as Sigurdsson saw a low shot deflected wide of goal in what was already a fast-paced second period.
Stoke made their first change of the afternoon with twenty minutes to play as Charlie Adam made way for Stephen Ireland.
But the Swans saw their dominance and persistence pay off with the opening goal with fifteen minutes remaining.
Jonjo Shelvey did well on the right flank to keep the ball in play before cutting and chipping a lovely cross to the far post where Jefferson Montero was waiting to stoop and head home from close range.
That prompted Garry Monk to make his second change of the afternoon as the impressive Nathan Dyer was replaced by Ki Sung-Yueng, while Stoke made a double change as Mame Biram Diouf and Jonathan Walters made way Peter Crouch and Peter Odemwingie.
And with five minutes remaining the visitors were reduced to ten men as Marc Wilson was shown a second yellow card for bringing down Montero as the winger outpaced the Stoke defence.
From the resulting free kick, Shelvey saw a fierce effort superbly tipped over the crossbar by England international Jack Butland as the home side looked for that crucial second goal.
Swansea made their third change in the final minute of normal time as Modou Barrow - back from his recent loan spell at Nottingham Forest - replaced the lively Montero.
But it was another substitute - Ki Sung-Yueng - who wrapped up all three points in stoppage time as he side footed home from eight yards out after Shelvey's cut back.
The victory was the Swans' ninth at home this season; one better than the eight that were achieved in the 2011-12 season.