Two goals inside the last 11 minutes saw West Brom inflict a first home defeat on the Swans in 2010.
A Graham Dorrans spot-kick and last minute strike from substitute Ishmael Miller were enough for the visitors to dent the hosts' chance of chasing automatic promotion.
Controversy surrounded the 79th minute penalty when Angel Rangel was adjudged to have fouled Giles Barnes inside the area but the referee showed no hesitation in pointing to the spot and Scottish international Dorrans kept a cool head to break the deadlock.
And as the Swans committed men forward searching for a late leveller the Baggies struck the killer blow against the run of play with Dorrans setting-up Miller for the second.
Garry Monk made his return to the Swansea City line-up following a calf injury.
The captain last featured in last month's draw at Plymouth Argyle and came in to replace youngster Jazz Richards; Monk moved into the centre while Alan Tate switched out to left-back.
Wide-man Cedric van der Gun and Nathan Dyer returned to the fold in place of David Cotterill and Tom Butler while Shefki Kuqi, who scored the winner at Watford seven days earlier, was back in attack in place of Craig Beattie.
Gorka Pintado was also back in the squad after the striker completed his four-match ban at the weekend.
Swans:Dorus de Vries; Angel Rangel, Garry Monk(C), Ashley Williams, Angel Rangel; Leon Britton (Guillem Bauza, 86'), Mark Gower (Craig Beattie, 80'), Darren Pratley, Nathan Dyer (David Cotterill, 79'), Cedric van der Gun; Shefki Kuqi.
Not Used:David Cornell (GK), Jazz Richards, Lee Trundle, Gorka Pintado.
West Brom: Scott Carson (C), Gabriel Tamas, Abou Meite, Marek Cech, Jonas Olsson (Gianni Zuiverloon, 46'), Robert Koren, Ben Watson, Youssouf Mulumbu, Graham Dorrans, Chris Brunt (Giles Barnes, 70'), Luke Moore (Ishmael Miller, 65').
Not Used Dean Kiely (GK), Joe Mattock, Simon Cox, James Morrison.
Attendance: 17,774 Away: 1,025
The atmosphere inside the Liberty Stadium was electric as two of the top four Championship sides lined-up for this exciting affair.
A late surge of fans packed themselves into the ground for the start of this encounter of which the home side enjoyed the lions' share of possession.
And within the first five minutes the Swans were handed two opportunities to deliver the ball into the box from the set-pieces - the first a corner which was cleared by the Albion defence, but Mark Gower's second attempt from a free-kick saw the midfielder pick out Garry Monk, the defender returning from injury, to connect with a header but he flashed it across the face of goal.
The game had to wait until the 13th minute for its first concrete attempt at goal, however, as Nathan Dyer outmuscled Youssouf Mulumbu off the ball on the edge of the area but curled his effort over the top of Scott Carson's goal.
West Brom rallied but offered no threat on Dorus de Vries and his defence as they attempted to counter attack down the left-hand side, while Dyer had the crowd on their feet with 21 minutes played when his low cross from the right somehow evaded Carson and clattered the outside of the post.
And the visitors were even showing early signs of frustration as the home side played keep ball and this resulted in Scottish midfielder Graham Dorrans picking up the game's first caution of the evening shortly before the half-hour for a foul on Angel Rangel.
Minutes later and the Swans were back on the offensive, this time Mark Gower fancied his chances from 25-yards out but could only hit the North Stand.
And they continued with constant pressure for the remainder of the half and with a little over five minutes to play until the break Shefki Kuqi showed great speed and strength to create another opening.
Abou Meite held the ball inside his own half and had option to pick out but Kuqi charged in from nowhere to challenge the defender from behind, robbing him of possession and sending Cedric van der Gun down the left.
The Dutchman carried the ball to the by-line and delivered a dangerous cross which was missed by both sets of players but Dyer did come within inches of connecting inside the six-yard box.
Mark Gower did have the final say of the half when he tried his luck with a free-kick from just outside the area but he was unable to hit the target.
Half-Time: Swans 0 West Brom 0
The visitors made a very strong start to the second period and within five minutes of the re-start Dorus de Vries was forced into making his first stop of the evening,
Graham Dorrans orchestrated the move which started with the Scotsman striding through Swansea's midfield before picking out Luke Moore to the left out goal and his strike tested the Dutchman from the angle who had to push the ball to safety to concede a corner.
Alan Tate had the home side's first 'half-chance' short;y afterwards when a Mark Gower corner was taken off his foot inside the area, but he was able to compensate just after the hour when he cut inside his man 25-yards from goal to shoot but Carson was equal to his effort.
The England international 'keeper was forced into saving again two minutes later from Nathan Dyer, who'd jinkxed his way past four Albion defenders before firing straight at Carson.
Despite continuing to control this half the Swans defence were having to deal with the threat of substitute Ishmael Miller in attack whiie Gabriel Tamas went close with a header from a corner.
But they say that football can sometimes be a cruel, cruel game, and this was displayed 11 minutes from time when the Baggies were awarded a penalty.
Many would question the decision to award substitute Giles Barnes the spot-kick after going down under a challenge from Angel Rangel but the match official duly pointed to the spot and Graham Dorrans stepped up to slot the opener past de Vries.
And despite their best efforts to seek a leveller the Swans were caught out by a last minute counter attack which led to the Baggies scoring again.
Ishmael Miller beat the offside trap to latch on to Dorrans' through ball and after gliding past de Vries to striker slotted into the bottom corner.