Having lost to Manchester United and Tottenham, Michael Laudrup's side were in need of a result to lift them off bottom spot and duly delivered with Hernandez teeing up Davies for the opener before applying the finishing touch in the 83rd minute.
Swansea had started lethargically, but West Brom failed to convert a lively start into goals and paid the price when Davies' second career goal left them chasing the game.
They could not find a way back into it as the game progressed and instead found themselves opened up at the back in the closing minutes.
While Swansea's campaign is now up and running, Albion head into the international break with one point from three matches.
The day had started with Steve Clarke confirming Nicolas Anelka's return to the fold, less than two weeks since his mooted retirement, by including the striker in the starting XI.
His name was the most notable on Clarke's team sheet but there was also a first league start for on-loan Manchester City winger Scott Sinclair, against his old club.
Swansea showed six changes from the side that took on Petrolul Ploiesti in Europa League qualifying, with a handful of senior men restored.
Wilfried Bony won a dangerous free-kick for Swansea after just two minutes, Jonjo Shelvey curling his effort over the crossbar from just outside the area.
But otherwise, the opening stages were all about West Brom.
Source: PA
Source: PA