The Capital One Cup holders lifted themselves off the foot of the Premier League table courtesy of an influential outing from their Spanish winger, while the Baggies remain winless
Ben Davies opened the scoring for the away team in the first half, neatly volleying the ball past Boaz Myhill, before Pablo Hernandez, who set up the first goal, wrapped up the three points late on.
Nicolas Anelka made his return to West Brom's line-up, following the death of a close friend that had seen him consider retirement according to manager Steve Clarke, while fellow newcomer Scott Sinclair made his league debut for the Midlands side.
Swansea boss Michael Laudrup, meanwhile, made six changes from the Swans' mid-week Europa League defeat to Romanian outfit Petrolul Ploiesti, while record-signing Wilfried Bony made his first league start.
|By Tom Davis
West Brom and Swansea had only scored one goal in the league between them prior to kick-off and with both sides lumbering at the foot of the table, this really was a day set up for strikers.
But left-back Ben Davies had other ideas when he opened the scoring to give the visitors the lead with a run from deep.
Nicolas Anelka looked a different player to the man we saw against Southampton last time out but the home side still failed to find the net.
Pablo Hernandez ended any hopes of a comeback when he doubled the Swans' lead to give the Michael Laudrup's men their first points of the campaign.
James Morrison's header was nervily cleared away as the hosts looked to grab a foothold in the game, but they could not hold off the Welsh side, who went ahead on 22 minutes.
Hernandez burst down the right and clipped a cross into the area with Davies latching onto it and lashing a wondrous volley past Myhill.
Bony, yet to find the form he showed in Holland, had a chance to double Swansea’s advantage minutes before the break, but the 24-year-old saw his effort comfortably scooped up by Wales international Myhill.
And, despite Clarke's efforts to alter the flow of the game by introducing Graham Dorrens at half-time, Swansea came out for the second period in much the same vein as they ended the first.
Wayne Routledge had a chance to extend the away side's advantage within three minutes as he tore down the wing, but a slightly heavy touch cost him as Myhill managed to keep him out.
The frustrations then continued to heap up for the hosts, with Anelka growing increasingly more agitated as his impressive work-rate continued to reap no rewards and the home side struggled to organise themselves.
And it only got worse for the Baggies; Hernandez saw an effort bounce off the top crossbar, but was unperturbed as he found the back of the net moments later after picking up Michu's clever cut-back into the area.
Clarke's side remain without a league goal this season, with just a point to show from their opening three games, while Swansea climbed off the bottom of the league with their first victory of the new campaign.