Dyer put the Swans ahead after only two minutes after a back-heel by Gylfi Sigurdsson into the box. Jonas Olsson slipped and allowed Dyer to latch onto the ball and he slotted home from a tight angle on the right.
Wayne Routledge then doubled the hosts’ advantage on 24 minutes with a fantastic volley from the edge of the box after Craig Dawson headed the ball into his path.
West Brom improved after the break but Dyer made sure of the win with a low effort with 19 minutes remaining following a Sigurdsson flick-on as Garry Monk’s side maintained their perfect start to the campaign.
But Swansea were also aided by some pitiful defending, with West Brom still seeking their first league victory under new manager Alan Irvine.
Monk’s side had the perfect start inside two minutes when Dyer picked up Wilfried Bony's lay-off and drove towards the Albion area.
Dyer found Sigurdsson and he took advantage of the Icelandic midfielder's clever back-heel return and Olsson's untimely slip to score his second goal in as many Premier League games.
It was a high-tempo start from a Swansea side buoyant after opening wins over Manchester United and Burnley, and Bony and Jonjo Shelvey both tried their luck from distance against Albion opponents struggling to get a foothold in the contest.
Bony headed over Shelvey's cross with West Brom temporarily reduced to 10 men with Olsson off the pitch, but Swansea doubled their lead after 24 minutes with a goal to remember.
Sigurdsson centred following Chris Brunt's poor clearance and, although Dawson was first to the ball, his header lacked distance.
Routledge was onto the dropping ball in an instant and with both feet off the ground he fizzed an 18-yard volley past the helpless Foster.
It almost got worse for Albion when Olsson headed Routledge's cross onto his own crossbar and there was no threat from the visitors until club record £10m signing Brown Ideye, making his first Premier League start, sent in a low shot which Swansea goalkeeper Lukasz Fabianski held comfortably.
Routledge almost added another spectacular effort in the closing stages of the first half when Albion failed to clear a free-kick and the winger flashed a volley just over from 18 yards.
West Brom showed more appetite for the fight at the start of the second period but they were fortunate to escape when Dyer found space down the right for the umpteenth time and rolled a ball into the box which Bony was just unable to connect with.
Swansea were a real threat on the counter every time a West Brom attack broke down and Routledge led the charge when Brunt lost possession.
Routledge got a return pass off Bony and his cross would have found the lurking Sigurdsson but for a fingertip intervention from Foster.
Stephane Sessegnon's half-time arrival appeared to pep up Albion and the game was more of an even contest, albeit scrappy for some periods and tackling which could be described as dubious at best.
But Ki fired straight at Foster and then there was controversy when referee Paul Tierney, in charge of his first Premier League game, adjudged that Dawson's intervention to stop Bony escaping was a deliberate back-pass to his goalkeeper.
Bony took the resulting free-kick from 12 yards and his effort was blocked on the line by what appeared to be the right arm of full-back Andre Wisdom, before his follow-up shot was saved by Foster.
Tierney waved away Swansea's penalty protests and Bony was out of luck again when he raced onto substitute Jefferson Montero's pass but blazed over from inside the box.
But Swansea were not to be denied and it was the same Sigurdsson-Dyer combination for the first goal which again paid off after 71 minutes.
Angel Rangel played the ball into Sigurdsson in midfield and he was allowed time and space to pick out Dyer who ran clear and finished emphatically past an exposed Foster.
Swansea were in total control but Jordi Amat's mistake at the near post was almost punished when Sessegnon fired against the bar and then Saido Berahino's shot was deflected inches wide of Fabianski's goal.
But Swansea comfortably saw out the rest of the game to make it nine points from nine.