CRAIG Beattie returned to haunt his former employers as his fine 50th-minute strike sentenced Albion to their second home defeat of the season.
On chances created, the Swans just about deserved their lead and the Welsh club then produced a terrific rearguard action to repel long spells of Baggies pressure.
Albion created enough chances to nick a point, with Chris Wood and sub Simon Cox both going close at the death.
But Beattie's solitary strike proved enough to shade the first league meeting between the two clubs in 16 years as the Swans stretched their unbeaten run to seven games.
Roberto Di Matteo rang one change from Saturday - Wood replaced back-injury victim Roman Bednar - as first entertained 16th.
Di Matteo's former Serie A rival Paulo Sousa made two changes to his Swans team, with Marcos Painter and Cedric van der Gun coming in for Federico Bessone and Andrea Orlandi.
Beattie was given a warm welcome by the Hawthorns hordes on his first return since moving to the Liberty Stadium in an £800,000 deal two months ago.
Albion's players paid tribute to former inside forward Dave Burnside, who died suddenly on Saturday evening, by wearing black armbands.
The game started at a furious pace as both sides knocked the ball around with great composure.
However, less could be said about three long-range efforts from Graham Dorrans inside the opening 11 minutes, which all sailed high and wide of Swansea keeper Dorus De Vries' goal.
Albion created the first moment of panic in either box on 15 when only Alan Tate's sliding interception denied Moore a certain goal from Gianni Zuiverloon's dangerous cross.
The Baggies were slowly getting on top and Saturday's two-goal hero Jerome Thomas had loud penalty appeals turned down when he appeared to be body-checked by Tate as he charged into the box.
Swansea broke straight upfield and Beattie came within inches of getting on the end of Angel Rangel's terrific near-post centre.
It wasn't hard to see why the visitors started the game with the joint-second meanest defence in the division as they continually denied Albion space in and around their penalty area.
And Thomas summed up the hosts' sense of frustration when he curled a 20-yard free-kick well off target.
However, Scott Carson was the first keeper to be called into action when he produced a goal-saving block on 30.
The England keeper did superbly to deny Nathan Dyer at point-blank range after Beattie had pulled the ball across the face of goal following a swash-buckling run.
Back came Albion and Wood was mightily unlucky not to break the deadlock when he volleyed inches over at full stretch from the impressive Gonzalo Jara's exquisite centre.
Carson managed to top his earlier save on 38 with a brilliant one-handed stop to deny Tate's downward header from Mark Gower's corner. He was then alert to pounce on the loose ball.
Swansea were becoming increasingly dangerous and van der Gun should have done much better when he exchanged a one-two with Gower before curling high and wide from 15 yards.
Former Albion youth player Ashley Williams then had his head in his hands after planting a free header from Gower's corner straight at Carson.
The Baggies were relieved to still be level as the half reached its conclusion, although Moore went mightily close in the dying seconds at the other end.
The striker's acrobatic volley from Jonas Olsson's flighted ball into the box looped over De Vries and dropped inches wide of the far post.
Di Matteo didn't waste any time making changes, replacing Moore and Marek Cech with Robert Koren and Filipe Teixeira during the half-time interval.
The substitutions helped spark a spell of sustained Albion pressure - only for Swansea to break the deadlock against the run of play on 50.
Gower slotted Beattie in with a slide-rule pass and the Scotland international beat Carson with a clinical 15-yard drive which nestled inside the far corner of the net.
Albion regrouped and De Vries had to pull off an acrobatic punch to prevent Koren getting on the end of Zuiverloon's cross-cum-shot.
The Baggies were now camped inside the Swansea half but were finding their opponents' red defensive wall virtually impenetrable.
So much so that long-range efforts became the order of the day and De Vries had no trouble holding onto Wood's 25-yard grass-cutter.
Di Matteo made his final throw of the dice on 74 as he sacrificed a defender for a forward by replacing Joe Mattock with Cox.
And the former Swindon marksman almost made a telling impact inside two minutes.
Dorrans and Youssouf Mulumbu hunted down Darren Pratley to win the ball back and the latter threaded Cox through, only for the pint-sized striker to drag his shot inches wide of the far post from 15 yards.
With Albion throwing players forward, they were always susceptible to the counter-attack and Carson pulled off a world-class save to deny sub Thomas Butler, pushing his fierce 12-yard drive onto his far post.
The Baggies continued to throw the kitchen sink at Swansea in the dying seconds and Thomas saw an 18-yard shot fly just wide after cutting inside Rangel.
There was even more agony in the 92nd minute when makeshift striker Olsson flicked on Dorrans' aerial ball and Wood glanced wide from close range.
With that chance went Albion's hopes of snatching a point their second-half pressure deserved.
ALBION (4-4-2): Carson; Zuiverloon, Jara, Olsson, Mattock (Cox 74); Cech (Teixeira HT), Mulumbu, Dorrans, Thomas; Moore (Koren HT), Wood. Subs not used: Kiely (gk), Meite, Martis, Reid.
SWANSEA (4-1-4-1): De Vries; Rangel, Tate, Williams, Painter (Richards HT); Britton; Dyer (Butler 61), Pratley, van der Gun, Gower (Allen 74); Beattie. Subs not used: Cornell (gk), Lopez, Trundle, Idrizaj.
GOALS: SWANSEA - Beattie (50).
BOOKINGS: SWANSEA - Painter (persistent fouling 35), Pratley (foul 78).
REFEREE: A D'Urso (Essex).
ALBION STARMAN: Gonzalo Jara.