Dyer sinks Burnley as Swansea maintain winning start
Garry Monk's team had enjoyed a shock win against Manchester United on the opening day of the new Premier League campaign and Dyer's first half strike was enough to claim another three points in a hard-fought clash at the Liberty Stadium.
Burnley had been beaten by Chelsea in their first game back in the top-flight on Monday and Sean Dyche's side remain without a point despite a battling display that saw Swansea goalkeeper Lukasz Fabianski produce an excellent second half stop to deny David Jones and preserve the win.
The Swans were unchanged following their shock victory at Old Trafford, with midweek signings Federico Fernandez and Tom Carroll not included in Monk's squad.
They went close to taking a third-minute lead when Wayne Routledge's cross found Wilfried Bony 12 yards out.
The Ivory Coast striker's header seemed destined for the far corner of the net but Burnley defender Jason Shackell intervened to clear the danger.
Routledge then sped past Kieran Trippier to deliver the perfect ball for Gylfi Sigurdsson, yet the Icelandic midfielder's shot lacked power and Burnley goalkeeper Tom Heaton held on.
But Heaton was beaten in the 23rd minute as Ben Mee failed to intercept Sigurdsson's ball and Dyer advanced to shoot past the goalkeeper's weak attempted save at his near post.
Bony had another chance straight after the restart when Dean Marney's headed back pass fell into his path but he horribly miskicked as he bore down on goal.
Danny Ings' drive was deflected wide as the Clarets came into the game more in the second half.
And Burnley should have been level when Marney's 64th minute cross picked out the unmarked Lukasz Jutkiewicz but the former Middlesbrough forward headed over.
Monk had seen enough and sent on Bafetimbi Gomis and Jefferson Montero for Bony and Dyer, but Burnley were within inches of equalising when Ings found Jones and his shot was saved by Fabianski.
Swansea nearly landed the killer second goal when South Korea midfielder Ki Sung-yeung's rising drive just cleared the crossbar, but the hosts had already done enough.