Goals from Jefferson Montero and Ki Sung-yueng secured all three points for the Swans, while Marc Wilson was sent off late on for Stoke after receiving a second yellow card.
It was a forgettable affair for long spells but the win solidifies Swansea’s hold on eighth spot as they move six points clear of Stoke in ninth, the Welsh club on course for their highest-ever Premier League finish.
Poor execution in the final third was a feature of the first half as both teams struggled to break each other down.
Swansea’s best move of the half came in the 42nd minute when Montero found the overlapping Neil Taylor down the left and the Welsh defender whipped in a cross which Dyer layed off to Shelvey on the edge of the box but his shot is straight at Butland.
Stoke came very close to opening the scoring just before the break when Steven N’Zonzi neatly evaded Gylfi Sigurdsson’s tackle on the edge of the box before curling a shot towards the top corner which Lukasz Fabianski did well to tip over.
Garry Monk must not have been impressed with his side’s first-half efforts because Swansea came out with much greater purpose for the second half.
They almost took an immediate lead when Angel Rangel drove into the box from the right flank and laid the ball off to Sigurdsson but his curling shot from the edge of the box cannoned off the crossbar.
Sigurdsson missed a gilt-edged opportunity moments later when Nathan Dyer made a driving run down the right and clipped a cross in from the byline which the Iceland international somehow managed to head over from six yards out when completely unmarked.
Swansea continued to press and they finally made the breakthrough on 76 minutes thanks to some great play from Jonjo Shelvey.
The former Liverpool man did well to keep the ball in down the right before stepping inside Erik Pieters and sending an inviting cross to the back post with his left foot which Montero was on hand to nod home.
Peter Crouch and Peter Odenwingie were introduced for Stoke soon after as Mark Hughes’ side pushed for an equaliser.
But they were made to pay by Swansea as they were caught high up the pitch and Wilson was forced to hack down Montero as he was through on goal to earn himself a second yellow.
Swansea wrapped up all three points in added time when Shelvey found space in the inside left channel and laid the ball off for Ki to sidefoot past Jack Butland.
Soccer Saturday verdict – Phil Thompson
“First half wasn’t very good – both teams – there wasn’t a lot to shout about. It was a lot better in the second half. This Swansea team have got a lot of good players, Sigurdsson and Shelvey. It got going in the second half. This is 53 points for this team, for Garry Monk. It’s been a very, very good season. The first goal was brilliant, Jonjo Shelvey is the creative brilliance in this side.
“It took until the 92nd minute before they wrapped it up. Ki is in great goalscoring form, and he just sidefooted it past Butland.
“Jonjo Shelvey is learning to play. I think it was earlier in the season when Garry Monk had words with him, or told the media, and said he needs to grow up in a football sense. He seems to have taken that on; he was always trying a Hollywood ball, a 50-yard ball. He makes this team tick.
“The second half just wasn’t enough from this Stoke side. They tried bringing Odemwingie on, Crouch came on, but it just wasn’t enough.”
Swansea: Fabianski (7), Rangel (7), Taylor (8), Williams (6), Fernandez (7), Cork (6), Shelvey (8), Montero (7), Dyer (6), Sigurdsson (6), Oliveira (5)
Substitutions: Emnes (6), Ki (7), Grimes (6)
Stoke: Butland (8), Bardsley (7), Shawcross (6), Wilson (5), Pieters (5), N’Zonzi (7), Whelan (6), Adam (5), Arnautovic (5), Walters (6), Diouf (5)
Substitutions: Ireland (5), Crouch (6), Odemwingie (5)
Man of the match: Jonjo Shelvey