The Swans continue to heap misery on West Brom as the Welsh side secure first points.
Ben Davies made the breakthrough with a brilliantly taken 22nd-minute volley and after Swansea resisted West Brom’s efforts to get back into the game, Pablo Hernandez sealed victory seven minutes from time.
Michael Laudrup’s side showed no ill effects from their trip to Romania to play Petrolul Ploiesti in the Europa League on Thursday, but Steve Clarke’s West Brom are still seeking a first win, and first goal, of the nascent campaign.
Nicolas Anelka was recalled to the West Brom starting XI after being granted compassionate leave following the death of a close friend, while Scott Sinclair was handed a full league debut against his former club.
Visitors Swansea made one change to the team beaten 1-0 by Tottenham Hotspur last weekend, with record-signing Wilfried Bony making his first league start in place of Jonathan de Guzman.
Swansea made the early running, Jonjo Shelvey and Michu going close from distance before Wayne Routledge saw a shot comfortably saved by West Brom goalkeeper Boaz Myhill, who replaced the injured Ben Foster.
West Brom should have taken the lead in the 20th minute when the unmarked James Morrison miscued his header from a Sinclair free-kick and two minutes later, Swansea made a stylish breakthrough.
Hernandez hooked the ball into the box from close to the byline on the right-hand side and Davies steamed in from left-back to steer an emphatic side-foot volley into the net.
Anelka looked menacing for West Brom and he came close to equalising 10 minutes later after sprinting clear and dragging a shot fractionally wide of the far post.
Routledge spurned an opportunity to double Swansea’s lead in the early stages of the second half, with a heavy first touch to control Michu’s pass enabling Myhill to block.
Clarke threw on strikers Saido Berahino and Markus Rosenberg in an effort to salvage something, only for Hernandez to kill the game off from Michu’s pass with seven minutes to play.