The Swans suffered a severe blow as West Brom came from behind to give Pepe Mel his first victory since taking over.
Garry Monk's side had got off to the perfect start as Roland Lamah fired them ahead after just two minutes at the Liberty, with the Swans wasting a string of chances in the first half.
But the Baggies bounced back in the second half and were far brighter.
Stephane Sessegnon fired into the bottom corner after 52 minutes to level the scores, and then - after Jonathan de Guzman saw his penalty appeal turned down - Youssouf Mulumbu curled his low effort in off the post with just four minutes left.
Defeat left the Swans on 29 points - four ahead of third-bottom Sunderland, who had played two games less.
The Swans made three changes to their starting XI.
With Chico Flores serving a one-match ban following his dismissal in the 1-1 draw with Crystal Palace last time out, fellow Spaniard Jordi Amat partnered captain Ashley Williams in central defence.
Roland Lamah made his first start in the league since the draw at Aston Villa on December 28 as Nathan Dyer missed out with a slight ankle complaint.
The final change saw head coach Garry Monk bring Jose Canas into midfield as Pablo Hernandez moved to the bench.
Also included among the substitutes was Spanish international Michu, who hoped to make his first appearance since December 15 following an ankle problem.
SWANS:Michel Vorm, Angel Rangel, Jordi Amat, Ashley Williams (capt), Ben Davies, Leon Britton (Marvin Emnes, 87), Jose Canas (Michu, 63), Jonathan de Guzman, Wayne Routledge, Roland Lamah (Pablo Hernandez, 76), Wilfried Bony.
SUBS: Gerhard Tremmel, Dwight Tiendalli, Neil Taylor, Leroy Lita.
WEST BROM: Ben Foster, Craig Dawson, Gareth McAuley, Jonas Olsson (capt), Steven Reid, James Morrison, Youssouf Mulumbu, Graham Dorrans (Zoltan Gera, 75), Liam Ridgewell, Stephane Sessegnon (Thievy Bifouma, 80), Victor Anichebe (Liam O’Neil, 89).
SUBS: Boaz Myhill,Matej Vydra,Saido Berahino, Scott Sinclair.
In perfect conditions at the Liberty, the Swans got off to the perfect start as they took the lead after just two minutes.
Wilfried Bony threaded through a delightful pass for Roland Lamah to chase on to, and the Belgian international latched onto the ball inside the box and cut back onto his weaker right foot before directing his low effort into the bottom corner.
West Brom went in search of an instant reply, and the powerful Victor Anichebe wriggled free of Ashley Williams to latch onto a through ball but his shot flew straight at Michel Vorm.
But it was the Swans who went close to getting the second goal of the game after 18 minutes as Leon Britton linked with Ben Davies to find Lamah down the left, and when his cross found Bony, the striker's effort bounced off the chest of keeper Ben Foster before it was cleared from danger.
The Baggies kept plugging away, and Stephane Sessegnon fired high and wide after turning Davies from 20 yards out.
It was end-to-end stuff, and Lamah was only denied by a perfectly-timed block in the Baggies box after Routledge's cross had been cleared into his patch.
The winger was at it again soon after, with Lamah heading a Jonathan de Guzman corner wide at the far post.
It was pulsating stuff at the Liberty, and another chance went begging as Routledge beat his marker before firing a low bouncing cross along the face of goal but de Guzman failed to connect when sliding in at the back post.
The chances kept coming, and two arrived within the space of 40 seconds.
Firstly, Bony chested down a high Routledge cross before volleying wide inside the box and then de Guzman steered Lamah's low centre after the Dutchman had latched onto Foster's under-hit goalkick.
And, with the game heading towards the break, another opportunity passed the Swans as Williams lost marker Jonas Olsson to meet a de Guzman corner, but the skipper's header bounced off the surface and onto the top-netting.
HALF-TIME: Swans 1 West Brom 0
Just as the Swans had made a fine start to the first half, West Brom themselves made the perfect start after the restart as they were on level terms in the 52nd minute.
Sessegnon found himself in space at the edge of the area and he blasted his effort low into the bottom corner with Vorm beaten at full stretch.
The Swans looked for an instant reply as de Guzman's free-kick curled over the wall, but Foster leapt to his right to catch the Dutchman's effort.
The Swans thought they had a strong case for a penalty when de Guzman's volley struck the arm of Gareth McAuley, but referee Martin Atkinson waved away the appeals.
Garry Monk made his first change just past the hour mark as Michu came on in place of Jose Canas.
Both teams were pushing hard for the lead, and de Guzman was denied by the legs of Foster after he ran into the box leaving Olsson and Youssouf Mulumbu behind.
Another Swans change saw Pablo Hernandez replace scorer Lamah, who hobbled off with a hip injury.
But the Baggies stunned the Swans with five minutes left.
After the home side failed to clear their lines, Mulumbu powered on without a challenge and coolly curled home past Vorm via the inside of the post.
It stunned the Liberty, and the Swans needed a reaction quickly.
Monk threw on Marvin Emnes in place of Britton as they went in search of a leveller.
But the equaliser never came as West Brom celebrated their first victory under Pepe Mel.