A Danny Graham strike secured Swansea City just their second Premier League away win of the season as West Bromwich Albion's poor home run continued.
Marc-Antoine Fortune put the Baggies ahead, firing in Jonas Olsson's flick from a corner, as West Brom sought a first home league win since November.
But Gylfi Sigurdsson inspired an immediate comeback as he calmly slotted home Neil Taylor's cross.
We were not good enough - Hodgson
Graham won it with a third goal in five minutes, guiding in Sigurdsson's pass.
The striker's 10th goal of the season moved Swansea back into the top 10 on 30 points, while Roy Hodgson's side remain on 26 points, six points clear of the relegation zone but now on a run of four home defeats in a row.
Swansea brought the division's worst away record to a snowy Hawthorns but secured a second successive win from trips to the West Midlands following their triumph at Aston Villa in January.
Their task might have been harder had referee Jonathan Moss awarded the hosts an early penalty as Gareth McAuley's close-range header seemed to hit Swans defender Ashley Williams on the arm, but the unofficial was not convinced.
WEST BROM v SWANSEA FACTS
West Brom now have the joint worst home record in the Premier League, along with Wigan
West Brom have not won a Premier League match in February since 2006, a 2-0 win over Blackburn
Swansea are unbeaten in visits to the West Midlands this season, winning two and drawing one
Swansea have won only nine of their 30 points this term away from home
22 of Swansea's 26 goals have been scored by Englishmen, only Manchester United can better that
And while Sigurdsson's impact was to prove crucial in attack, it was no less important that he headed Peter Odemwingie's first-half effort off the line. Fortune's goal-bound follow-up was blocked.
In a largely uneventful first half, an off-the-ball scuffle between Williams and Odemwinge might have proved a flashpoint but went unseen by official Moss.
The second half quickly sparked into life, however, with three goals inside five minutes just before the hour.
Fortune's first top-flight goal in 12 months sent relief around The Hawthorns, the French striker firing past Swans keeper Michel Vorm from a tight angle after Olsson had flicked on Graham Dorrans's left-wing corner.
But relief was short-lived as Sigurdsson levelled within 37 seconds of the restart.
The midfielder passed Taylor's teasing low cross past Baggies keeper Ben Foster for his first Swansea goal since
his arrival on loan from Hoffenheim,
but the former Reading man's third in as many games against West Brom.
Rodgers revels in 'brilliant' win
The Iceland international - appropriately excelling in the freezing conditions - then turned provider with a cross whipped in from the right that Graham managed to steer into the corner with his left foot.
Graham was denied a chance to extend Swansea's lead thanks to great covering by Olsson, the West Brom defender getting to Taylor's low left-wing cut-back before the Swansea top-scorer.
Odemwingie should have equalised late on for West Brom but missed the target with the goal at his mercy after a lovely flighted ball from Dorrans.
And Swansea clung on to their lead despite another superb chance for Fortune as his injury-time shot squirmed under Vorm's body but went wide.
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