The Baggies struggled early on and fell behind on 22 minutes when Swansea full-back Ben Davies raced forward to break the deadlock with an assured volley.
Swansea confidently kept possession after the break and doubled their advantage late on through Pablo Hernandez, who tucked home after hitting the crossbar moments earlier.
Here Sports Mole looks at what went wrong for Steve Clarke's side, who were outplayed for long spells as Swansea got their first points of the campaign.
On target 1
On target 4
Was the result fair?
Without question. Not only did Swansea largely dominate in midfield as we have come to expect, their passing in the final third had purpose and penetration. West Brom were unable to boss a congested middle third and paid a heavy price.
After a shaky start to the season Swans boss Michael Laudrup will be delighted with his team's response today. The visitors used Jose Canas and Jonjo Shelvey as buffers in midfield to great effect, allowing Angel Rangel and Davies to bomb on throughout the 90 minutes. Pablo Hernandez also took up intelligent positions to link up with Michu and Wilfried Bony, so plenty of positives for Swansea to build on before the international break.
West Brom's performance
Manager Clarke will be scratching his head after watching West Brom go a third game without scoring. Nicolas Anelka's efforts were a rare bright in an anonymous Baggies attack, with Scott Sinclair failing to make an impact on his debut. Defensively there were also huge questions marks as the Baggies regularly conceded possession cheaply and dropped too deep, allowing Hernandez in particular to exploit the space provided.
Sports Mole's man of the match
Pablo Hernandez: The Spanish winger just pips Davies and Jose Canas with an exemplary display. Hernandez broke with assured touch and intelligence throughout the match, while also regularly tracking back to stop Liam Ridgewell offering anything on the overlap. On this evidence Swans fans might be cheering another Spaniard's name at the Liberty Stadium for much of this season.
Mike Dean issued seven yellow cards on a busy afternoon at The Hawthorns, but in fairness he helped to keep play moving with a decisive streak. The official also did well to deal with Michu after an angry exchange with Claudio Yacob, calming the situation down and showing leniency to let the Argentine stay on the field.
Clarke will have to take this award for his decision to throw Scott Sinclair in from the outset. The winger struggled throughout and was clearly off the pace, with the Scot perhaps too desperate in his attempts to look for a new creative spark in the final third. Without Romelu Lukaku in the final third, West Brom are desperately struggling for ideas.
West Brom: A trip to Craven Cottage is next up for West Brom on September 14, as they take their search for the first goal of the season to West London.
Swansea: Laudrup's men host in-form Liverpool on September 16, as they go in search of back-to-back victories and a first success of the season at the Liberty Stadium.