Swansea's on-loan midfielder Gylfi Sigurdsson played a major role in Brendan Rogers' side coming from behind to register only their second Barclays Premier League away win of the season at West Brom.
The Iceland international, who joined from Hoffenheim last month until the end of the season, cancelled out Marc-Antoine Fortune's opener and laid on the winner for Danny Graham.
The visitors dominated for long spells as they followed up their 1-1 home draw against Chelsea in mid-week with another impressive performance.
But Albion's woeful home record continued and they have collected just eight points at The Hawthorns compared to 18 on their travels.
Roy Hodgson's side were often left chasing shadows with Sigurdsson and Joe Allen pulling the strings in midfield and 10-goal Graham a constant threat.
Swansea were soon into their stride and created the first opportunity of the game.
Sigurdsson's shot was blocked from an Allen corner and the follow-up attempt from Angel Rangel was deflected just wide.
Baggies midfielder Youssouf Mulumbu was caught in possession and was relieved to see Allen drag his shot past the post.
James Morrison brought Sigurdsson down 25 yards out and the Swansea player took the free-kick himself and sent it just wide.
In a rare West Brom attack Gareth McAuley headed wide from a Nicky Shorey cross. Peter Odemwingie's control then let him down when he was found in space by Jerome Thomas.
The threatening Graham missed a good chance to put Swansea ahead after half an hour. Graham shrugged off the challenge of McAuley when challenging for a Leon Britton free-kick. But, from 12 yards out he shot wide when he should have at least tested Ben Foster.