Swansea climbed off the bottom of the Premier League as Wilfried Bony's late winner eased the pressure on head coach Paul Clement.
The Swansea boss had insisted before West Brom's visit that his future did not rest on the outcome of this game.
But Clement's joy on the touchline was unconfined when Bony smashed home nine minutes from time in a crowded goalmouth to secure a 1-0 win.
It was the first time Bony, having scored at Stoke last week, had registered in back-to-back Premier League games since December 2014 - during his first Swansea spell.
But, more importantly, it takes Swansea above Crystal Palace at the foot of the table and to within one point of West Ham and West Brom.
This was Alan Pardew's second game as West Brom boss since succeeding Tony Pulis.
Pardew's last visit to Swansea 13 months ago was an incredible affair as his Palace side lost 5-4 in a game which hastened his departure from Selhurst Park.
That nine-goal thriller was never going to be repeated here with two teams short on creativity and confidence, and organised defence very much the strongest points of their game.
Swansea reverted to playing two wingers with Nathan Dyer and Wayne Routledge starting for the first time since Clement's first home game in January.
The plan was to provide a supply line to Bony but Swansea failed to manage a single on-target attempt in a first half devoid of entertainment.
Routledge did release Dyer through the middle but Ben Foster was out of his penalty area quickly to hack to safety.
Both sides had early opportunities with Mike van der Hoorn and Jonny Evans heading wide from set-pieces, and Jay Rodriquez's effort was comfortably handled by Lukasz Fabianski in the Swansea goal.
Kyle Naughton fired over from distance but Swansea went closer twice in the space of 60 seconds.
Jake Livermore diverted Ki's free-kick onto his post and Swansea kept the move alive for Routledge to find Alfie Mawson six yards out.
Mawson has a decent scoring record for a central defender, but this time he was unable to keep his header down.
The contest began to liven up after the break with Bony turning Evans to send a shot close to Foster's post and substitute Jordan Ayew firing over with his first touch.
Albion had sent on James McClean at the break and the Republic of Ireland winger produced a string of crosses which caused Swansea difficulties.
They also caught Swansea on the break but Hal Robson-Kanu wasted a glorious four-on-three advantage in Albion's favour.
Swansea managed their first attempt on target 15 minutes from time when Foster pushed Ayew's effort around the post.
Foster's save prevented an almighty row as play had continued with Robson-Kanu down injured and Pardew going berserk on the touchline.
Abraham should have settled matters in stoppage with only Foster to beat, but the miss did not matter as Swansea claimed their first win in two months.